The home side go into the weekend sitting just two points adrift of leaders and champions Manchester City, whereas Everton have climbed up to sixth in the table following their own upturn in form.
Liverpool manager Jurgen Klopp showed flickers of annoyance during his pre-match press conference for this game, more due to how his side's form is being perceived rather than frustration at the actual form itself.
A 2-1 defeat to Paris Saint-Germain in midweek left their Champions League hopes hanging by a thread, with last season's runners-up now facing the very real prospect of crashing out in the group stages and playing Europa League football after Christmas.
Matters are still in their own hands to a certain extent, but they would need to beat group leaders Napoli either 1-0 or by two clear goals later this month to book their place in the last 16.
The Reds will certainly need to put in an improved performance if they are to achieve that, but on the domestic front there is plenty to be happy about despite lingering questions over whether Liverpool are as fearsome an attacking outfit as they were last term.
Klopp's side had scored 15 more goals at this stage of last season, but a leaky defence undermined any potential title challenge in 2017-18 - something which has not been the case this term.
Indeed, Liverpool have conceded just five goals so far in 2018-19 - their lowest ever tally after 13 games of a top-flight campaign - while their points total of 33 is also more than they have accrued at this stage of any previous Premier League season.
It is now 14 games since Liverpool suffered defeat in the Premier League, including all 13 so far this term, while you have to go back to April 2017 for their last league defeat on home soil - 27 matches ago.
The Reds have won nine of their last 11 of those, with only Manchester City avoiding defeat so far this season, but most impressive of all is their defensive record at Anfield; 10 clean sheets in their last 11 outings and just one goal conceded since February - perversely against Cardiff City, who are the lowest away scorers in the division.
All of that bodes well ahead of Sunday's derby considering they have a formidable record against Everton at Anfield already, but Klopp has warned that this is the best version of the Toffees to visit during his tenure.
While that may be true, it could also be argued that this is the most complete Liverpool team to go into a derby in a generation, and they will be firm favourites to pick up a victory which should keep the pressure on Man City at the top.
Recent Premier League form: DWWDWW
Recent form (all competitions): WDLWWL
Four Everton managers have tried to break the Toffees' hoodoo at Anfield in the 21st century, and four Everton managers have failed.
Indeed, even more history would beckon if Silva did manage to pull off the feat this weekend as no Everton boss has won his first Premier League Merseyside derby since Joe Royle in 1994, and no Everton boss has ever won his first league game against Liverpool at Anfield.
The Portuguese manager has some precedent, though, having led Hull City to a win over Liverpool and Watford to a thrilling 3-3 draw against the Reds on the opening day of last season. Indeed, Silva is the only manager Klopp has faced at least twice in the competition but never beaten.
There is the added incentive of ruining Liverpool's unbeaten start to the season too, and the blue half of Merseyside will certainly be buoyed by the recent form ahead of the short trip across Stanley Park.
The Toffees have lost just one of their last seven Premier League matches, winning five of those with their only defeat coming at the hands of Manchester United at Old Trafford.
Everton have since held Chelsea to a goalless draw at Stamford Bridge, though, and may settle for a similar result against another unbeaten team this weekend considering the disparity between their away form and Liverpool's home record.
While the Reds have swept almost all before them at Anfield this season, Everton have won just one of their last seven away league games. Indeed, the 11-point gap between these two sides this season has been entirely made up on the road, with Everton having picked up as many points as their local rivals in home games.
It should be noted that Everton are in the midst of a devilishly hard run of away fixtures; Sunday's game is part of a six-match run on the road during which they face Arsenal, Manchester United, Chelsea, Liverpool and Manchester City.
One area Silva's side have improved as the season has progressed is in defence; the Toffees conceded 11 goals in their first six league games under the Portuguese boss, but have let in just four from their previous seven - including back-to-back clean sheets ahead of this match.
The visitors will be expected a much more difficult test on Sunday than their 1-0 win over Cardiff City last weekend, but a long overdue victory at Anfield could leave them only three points off the top four, depending on results elsewhere.
Recent Premier League form: WWLWDW
Recent form (all competitions): WWLWDW
Liverpool will be without captain Jordan Henderson after he picked up a red card against Watford last weekend.
A number of other players are understood to be carrying knocks following the midweek defeat to PSG, although Klopp did not disclose the identities of those doubts.
The Liverpool boss could opt to switch back to a 4-2-3-1 formation having seen his side struggle in a 4-3-3 system again in Paris, which is likely to mean a recall for Xherdan Shaqiri.
Mohamed Salah would lead the line in that scenario for his 50th Premier League appearance as a Liverpool player. A brace would see him equal the record for most goals in the first 50 Premier League games for a single club, currently held by Alan Shearer and Andy Cole on 41.
Everton, meanwhile, have no new injury concerns and could name an unchanged team to the one which beat Cardiff last weekend.
Liverpool possible starting lineup:
Alisson; Alexander-Arnold, Gomez, Van Dijk, Robertson; Milner, Wijnaldum; Shaqiri, Firmino, Mane; Salah
Everton possible starting lineup:
Pickford; Coleman, Keane, Mina, Digne; Gomez, Gueye; Walcott, Sigurdsson, Bernard; Richarlison
Head To Head
It is now 18 Premier League visits since Everton last beat Liverpool at Anfield, stretching back to September 1999 when Kevin Campbell scored the only goal of the game. The Toffees have drawn nine and lost nine since.
Everton's poor record in this fixture is not only exclusive to Anfield, though; they are currently enduring their longest ever winless run against Liverpool having failed to win any of their last 17 meetings home or away since 2010.
This match will be the 100th top-flight Merseyside derby to be played at Anfield, with Liverpool having won 43 of the previous 99 with 33 draws and 23 defeats.
We say: Liverpool 2-0 Everton
Everton are improving under Silva, but it is hard to ignore their poor away form, their wretched record at Anfield and Liverpool's own unbeaten run on their own patch. We're going for a fairly comfortable home win.