As for the visiting Reds, Liverpool are in a commanding position in third place and are heading to London having recently qualified for the final of the Champions League.
Chelsea welcome Liverpool to Stamford Bridge knowing that nothing less than three points will do as they aim to put pressure on fourth-placed Tottenham Hotspur.
The Blues' late bid for a Champions League finish has been ignited courtesy of a few Spurs hiccups in April, and Conte's men are now five points behind Tottenham with three games left to play.
It will likely take a minor miracle for Spurs to give up fourth spot, but all that Conte's charges can do is secure maximum points from their final games to ensure that they are in a strong position to pounce should Mauricio Pochettino's men flounder in the closing stages of the campaign.
What could arguably be more pertinent, however, is Chelsea's pursuit of Liverpool, who occupy third place and find themselves six points clear of the Blues having played one game more. Should Chelsea defeat Liverpool and then win their remaining game in hand over Jurgen Klopp's side, the Blues would move level on points with the Anfield club.
Chelsea are now five games unbeaten since losing out to Spurs in the Premier League at the start of April. Following the home loss, Conte's men have gone on to pick up three victories and a draw, including an FA Cup semi-final win that has established a mouthwatering clash with Jose Mourinho's Manchester United at Wembley.
Just a few months ago Chelsea looked doomed to failure with the prospect of Conte potentially departing before the summer had even arrived. Victory against the Reds on Sunday could leave the Blues looking in a much healthier position than many would have hoped for: closing in on both Liverpool and Spurs, while also sitting on a spot in the final of the FA Cup.
Should Conte's charges want to keep the top-four race alive, Chelsea will need to improve on some troubling form against Liverpool in the Premier League. The Blues have not beaten the Anfield club in six games running in the top flight, drawing three and losing three against the Reds.
Since his arrival in January, French forward Olivier Giroud has started to show his ability to impact the final third at decisive moments for the Blues. Coming into the game, the 31-year-old has bagged four goals in his last five league starts against Liverpool.
Recent form: WLDWWW
Recent form (all competitions): LDWWWW
Klopp's men booked their place in the Champions League final for the first time since 2007 courtesy of a 7-6 aggregate win over Roma, capping off a season-defining run in Europe's elite competition.
Reds fans will have celebrated well into the small hours after coming away triumphant from the Stadio Olimpico. Klopp might be slightly concerned at the way his side gave away four goals in the second leg, but the prospect of a monumental final with Real Madrid will soften the blow of a rare defeat on the continental stage.
After several years floating in the margins, the former giants of Europe have shown some devastating counter-attacking work and clinical finishing to light up the Champions League, but Klopp will still be keen to ensure that his side appear in the tournament next term by wrapping up qualification via a strong league finish.
Liverpool will have lofty designs on defeating Madrid in Kiev to wrap up a historic season, but should they fall to defeat then a top-four finish will be the only softener come the end of the season.
The club's outstanding progress in Europe has arguably come at a cost domestically, where Liverpool will now have to play out the remainder of the campaign with a squad bereft of some key players and likely suffering from fatigue. Klopp will want to rest players to face Madrid, but the German coach does not have the ability to rotate ahead of some crucial league games.
Heading to the Bridge, Klopp will be well aware of his favourable fortunes in south London since arriving in the Premier League, having won both of his league visits to Chelsea. Should Liverpool win on Sunday, Klopp would become the first visiting manager to win on his opening three trips to Chelsea.
Liverpool's final league game sees them take on Brighton & Hove Albion, leaving Klopp knowing that a point against the Blues on Sunday will leave his side requiring a victory over the Seagulls to leave the Reds well and truly beyond Conte's grasp.
Recent form: WWDWDD
Recent form (all competitions): WWDWDL
Giroud's goal return of late has left Conte with a nice headache as the Italian is left to decide between the Frenchman and Alvaro Morata in attack.
Chelsea possible starting lineup:
Courtois; Azpilicueta, Cahill, Rudiger; Moses, Kante, Fabregas, Alonso; Hazard, Willian, Giroud
Liverpool possible starting lineup:
Karius; Alexander-Arnold, van Dijk, Lovren, Robertson; Wijnaldum, Henderson, Milner, Mane, Firmino, Salah
Head To Head
The last six league meetings between the clubs have seen Liverpool go unbeaten, winning three and drawing three against the Blues.
Klopp's Liverpool have won two on the bounce at Stamford Bridge and could become only the third side to win three in a row at Chelsea in the Premier League since Blackburn Rovers, who capped off a three-game winning run in 1996.
The teams have met on 51 occasions in the Premier League's history. Both sides have won 19 matches, each club sharing a record of 13 home victories and six away wins.
We say: Chelsea 1-2 Liverpool
Chelsea somehow still find themselves in the running to claim a top-four spot and that will drive Conte's charges to end the season as strongly as they can.
Coming off the back of three straight league wins will stand the Blues in promising stead, but they will be facing a side that they have been unable to beat in 540 minutes of Premier League football.
Liverpool will be travelling to London full of confidence after booking a place in the finals of the Champions League and will know that even a point would still leave them in a commanding position to seal a spot in the top four.