Boss Pep Guardiola revealed the good news at his press conference ahead of City’s trip to Liverpool on Sunday - a game which will come too soon for skipper Vincent Kompany.
Guardiola does not anticipate any other injury worries ahead of the match, although he will check on his players at Friday afternoon’s training session.
Jesus injured medial knee ligaments in the goalless draw at Palace on New Year’s Eve, but could be back ahead of schedule.
Guardiola said: “He was (this week) in Barcelona and the news is quite good. I think two or three weeks, against Basel in the Champions League, he could be ready.”
City are unbeaten in the Premier League so far this season but many commentators believe this could be the biggest test of the season to date, especially given our record at Anfield.
Watch: City’s last 10 goals against Liverpool
Guardiola, though, sees the match as an enjoyable challenge for his side, adding: “Of course if you want to achieve something that’s good and win titles you have to win these kind of games.
“This season we were able to do that but we still have to go to Anfield, to Tottenham - there are still lots of games to play.
“But Liverpool is such an important game, to realise again if we are able to do big things in this season, in important stages, in the Champions League.
“To see ourselves, when we arrive in Basel, knockout games - how is our behaviour? We did it in Stamford Bridge, Old Trafford, and we’ll see on Sunday how we do.”
Guardiola is expecting Liverpool to attack having encountered Jurgen Klopp’s teams many times.
“I met Jurgen when I was at Bayern Munich and he was always a guy who tried to play forward, and with no fear.
“They are playing at Anfield - I’m not expecting a team that will wait for what is happening - I’m pretty sure he will try and make his own game and I think it will be a good game.
“Hopefully we can do better than last season. That is our target, and to show courage. This kind of game shows how your mentality is. Life goes on the next day, we just need try to and play our game, play with personality and to play who we are.”
City have had an extremely difficult time of things at Anfield down the years so will be looking to buck that trend.
The Blues have just two wins from 50 visits in all competitions going back to the mid-fifties. The last win was in May 2003, when a Nicolas Anelka double snatched victory.
Jurgen Klopp’s Liverpool are unbeaten since October this season and have won their last three Premier League games, plus the FA Cup derby victory over Everton last time out.
City, though, are enjoying a record season and defeated Liverpool 5-0 at the Etihad Stadium this season.
The Blues are 15 points clear at the top of the table and remain unbeaten in the league.
