The Brazilian has been training with his new club for the past week but he has not yet been registered to play.
Pep Guardiola insists he will not rush Jesus, who was allowed to rest throughout the month of December and is building up his fitness.
A debut at Goodison Park would have been some introduction to English football, though he will have to wait for his first City appearance.
MAN CITY INJURIES
Leroy Sane and Fernando returned to full training this week, meaning they should both be in contention on Sunday.
Vincent Kompany has also been back in training recently and could be a part of Guardiola's squad. Kevin De Bruyne has missed the last couple of training sessions but it is thought he has an illness rather than anything too serious.
Other than that, Ilkay Gundogan is City's only other known injury - the German will miss the rest of the season with a cruciate knee ligament injury.
MAN CITY SUSPENSIONS
Fernandinho will serve the second match of his ban against Everton. He will also miss games against Tottenham in the league and either Crystal Palace or Bolton in the FA Cup.
Everton have no suspensions to worry about.
MAN CITY POTENTIAL STARTING LINE-UP
City will have had nine days to recover from their FA Cup win at West Ham by the time they kick off on Sunday, and will have six days until their Premier League meeting with Spurs.
That means Guardiola will pick his strongest possible team. The City players elected not to go for a warm weather training camp in the Middle East after that game at West Ham, instead deciding to stay in Manchester for training after being given the weekend off.
In theory, then, City's players should be in top condition for this match. With Fernandinho banned and Fernando back in training, the former Porto man is likely to deputise in midfield, potentially alongside Yaya Toure.
Pablo Zabaleta played in midfield against West Ham though Fernando and Toure seem more likely to start.
Kompany has been back in training of late and it has been especially tricky to predict Guardiola's defensive line-ups this season, but the Belgian is most likely to start on the bench, if he is deemed fit enough to travel to Liverpool.
That means John Stones could be set for a starting role on his return to Goodison, having left Everton for City in the summer.
Leroy Sane, who has not featured since he scored his first goal for the Blues in the win against Arsenal in December, could provide an injection of pace from the bench.
Everton find themselves in a patch of inconsistent form, having won four, drawn three and lost five of their last 12 games in all competitions.
They were knocked out of the FA Cup on home soil by Leicester City last weekend and their home record is as mixed as the overall picture, with three wins, three draws and three defeats from their last nine games at Goodison.
Ronald Koeman will hope Morgan Schneiderlin will come in an make an impact on the Toffees' form. The Frenchman sealed his move - which could rise from £20m to £24m - from Manchester United on Thursday and will be eligible to play on Sunday.
Romelu Lukaku will be Everton's dangerman up front, and it was his goal that earned a smash-and-grab point at the Etihad Stadium in October.
But the Merseysiders do have plenty of selection issues, with influential midfielder Idrissa Gueye on international duty with Senegal at the Africa Cup of Nations
Yannick Bolasie and Muhamed Besic are long-term absentees thanks to serious knee injuries, while young forward Dominic Calvert-Lewin is out with an ankle problem.
Goalkeeper Maarten Stekelenburg, who saved two penalties and produced a string of fine saves the last time the two sides met, is doubtful, as are James McCarthy and Bryan Oviedo.
BEST OPTA MATCH FACTS
Everton are winless in their last seven Premier League games against Manchester City (D3 L4). Prior to this run, they had won six of the previous eight (D1 L1).
The Citizens have won two of their last three games at Goodison Park, having lost the previous four to David Moyes’ Everton between 2010 and 2013.
Three of Everton’s last five goals against Manchester City in the Premier League have been scored by Romelu Lukaku.
Yaya Toure has been directly involved in six goals in nine previous Premier League appearances against the Toffees (three goals and three assists).
Raheem Sterling has been directly involved in nine Premier League goals for Man City this season (five goals, four assists), compared to eight in his first season at the club.
Idrissa Gueye will be missing for this game as he is away representing Senegal at AFCON 2017. Gueye has made the most tackles in the Premier League this season (93).
TV COVERAGE & KICK-OFF TIME
The game kicks off at 13:30 UK time on Sunday, January 15, and is available on Sky Sports 1 in the UK.