The Toffees have beaten Burnley and Newcastle United in their two matches since Ancelotti took control, while City will enter the clash off the back of a 2-0 win over Sheffield United.
City were outstanding last term as they held off the threat of Liverpool to win the Premier League title in spectacular fashion. However, unless something quite staggering happens over the next few months, Pep Guardiola's team will not be ending the 2019-20 campaign with the English title.
The Citizens have lost five of their 20 league matches this season, recording just 13 wins to sit third in the table with 41 points. They are only a point off second-placed Leicester but sit 14 points off the leaders Liverpool, who have a game in hand following their exertions at the Club World Cup.
Liverpool's form this term has been just staggering, winning 18 of their 19 league matches to top the table. Even if City had been at their best in recent months then it is difficult to imagine that they would have been even close to Jurgen Klopp's team, who appear destined to win the Premier League.
City suffered a 3-2 loss away to Wolverhampton Wanderers on December 27, with the latter coming from behind to triumph in front of their home supporters. Guardiola's team had beaten Leicester on December 21 to keep their slight title hopes alive, but the defeat at Molineux would have hurt the team badly.
The Citizens did return to winning ways against Sheffield United on Sunday, though, meaning that they have been victorious in five of their last six matches in all competitions.
City have also lost just three of their last 32 home games in the Premier League, recording 27 wins in the process. What's more, under Guardiola, they have won 52 of their 67 home games in England's top flight.
The Manchester giants have also been victorious in each of their last four Premier League matches with Everton, including a 3-1 success in the reverse game at Goodison Park back in September.
The Toffees have only actually won one of the last nine matches between the two teams in all competitions, while they have not overcome City on their travels since December 2010, which is an indication of the size of the task facing Ancelotti's side in their first match of 2020.
Everton, though, will enter the match full of confidence following successive Premier League wins over Burnley and Newcastle in the two matches since Ancelotti replaced interim boss Duncan Ferguson as head coach.
For all of the criticism that has come the team's way in recent weeks, they are unbeaten in their last five Premier League matches, picking up three wins in the process to move up the table.
As it stands, the Merseyside giants are 10th in the table with 25 points having won seven, drawn four and lost nine of their 20 matches during the 2019-20 campaign. They are now seven points above the relegation zone and sit just six points off fifth position, which is an indication of the type of season it has been in England's top flight.
Dominic Calvert-Lewin has scored three times in his last two appearances for the Toffees, which led to the 22-year-old receiving high praise from Ancelotti. The Englishman is likely to keep his spot in attack for this match, and he certainly has the tools to cause City's defence all sorts of problems.
Luring Ancelotti to Goodison Park was huge for Everton, and a positive result on Wednesday would lead the team nicely into a run of winnable games; their next five after this one are against Brighton & Hove Albion, West Ham United, Newcastle United, Watford and Crystal Palace.
Richarlison's form under Ancelotti has also been impressive, and the Brazil international has now scored eight times in 24 appearances for the Toffees this season. Manchester United are thought to be interested in his services, but the new Everton manager will reportedly block any bid that might arrive.
City are arguably as weak as they have been for a couple of years, and there is no doubt that the Merseyside giants will be confident of picking up a result under their new superstar manager.
Manchester City Premier League form: WLWWLW
Manchester City form (all competitions): WWWWLW
Everton Premier League form: LWDDWW
Everton form (all competitions): WDLDWW
Ancelotti opted for a back five against Burnley and that might again be the case here with Calvert-Lewin and Richarlison operating as the front two for the visitors.
Manchester City possible starting lineup:
Ederson; Cancelo, Garcia, Fernandinho, Zinchenko; De Bruyne, Gundogan, Rodri; Bernardo, Aguero, Sterling
Everton possible starting lineup:
Pickford; Coleman, Mina, Holgate; Sidibe, Sigurdsson, Davies, Delph, Digne; Calvert-Lewin, Richarlison
Head To Head
City lead the head-to-head 72 wins to Everton's 68, while there have also been 47 draws between the two teams.
As mentioned above, the Citizens have dominated the recent meetings - winning each of the last four Premier League encounters - and have not lost to the Toffees in England's top flight since January 2017.
We say: Manchester City 2-1 Everton
Everton are certainly capable of making it a very uncomfortable 90 minutes for City, but we are finding it difficult to back against a win for the champions. We fancy De Bruyne to find the back of the net in a 2-1 home success.