Jesus, 20, sustained the injury during City's trip to Selhurst Park, where the runaway league leaders were held to a 1-1 draw against Crystal Palace on New Year's Eve.
"Today he is going to play in part of the session, it's good news", Guardiola told a news conference.
Benjamin Mendy is the only other player missing, with the defender still recovering from a cruciate knee ligament injury.
"I don't know when he'll be ready definitely to be with us, with the team, but the first step is (to train)".
City withdrew their interest in the Algeria forward on transfer deadline day last month as they were unwilling to pay more than £60million for a player Leicester were valuing at £95million.
The former Barcelona gaffer went on to express his delight on the performance of English clubs in round 16 of the UEFA Champions League.
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Mehrabad is located in western Tehran and mainly functions as a domestic airport, although it also serves some worldwide routes. A local official said bad weather had hampered a helicopter search.
"I think the FA Cup there are a lot of surprises, not just this season or previous seasons, all throughout history you always have these kind of situation happen. It's great news for this country that the Premier League teams are doing so well in Europe".
It remains to be seen when Jesus will be ready to return to action but he could have an outside chance of featuring in the Carabao Cup final against Arsenal on Sunday week.
Thankfully for them, that looks to be the case as Pep Guardiola confirmed the player was to train today.
But Cook, bidding to lead the Latics straight back to the Sky Bet Championship in his first season in charge, said the City side moulded by Guardiola is an altogether different proposition. Without the ball he wasn't flawless. Meanwhile, it looks like Gabriel Jesus could be back sooner than it was initially reported with the Brazilian taking fantastic strides towards his recovery.
"Even if he doesn't win I have as much respect as when he wins because I think people have an influence in the game". After 26 games in the league they're 16 points clear with one defeat whilst playing a brand of dominant, attacking football not seen in a generation.