City released photographs of the France left-back participating in a session with his team-mates on Monday.
Mendy, 23, who has been out of action since suffering knee ligament damage and undergoing surgery in September, last week suggested he was close to a return.
“When I started my recovery, I had in mind the semi-finals of the Champions League,” Mendy told the club website, www.mancity.com.
“That was my goal, but I am coming back a bit quicker than expected originally so maybe it will be possible for me to return sooner than that. I believe in this.
“I think it’s possible for me to come back within four weeks. It’s not a good thing to come back too soon and you have to take your time.”
Pep Guardiola’s City have an enormous lead in the Premier League and are all but guaranteed a Champions League quarter-final slot after a 4-0 win against Basel in the first leg of their last-16 tie.
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