The Swiss defender was initially named in the starting lineup for the Citizens' 2-1 defeat at Tottenham Hotspur in the last 16 of the EFL Cup on Wednesday night.
However, Akanji was forced to pull out of the first XI after sustaining an injury during the warm-up moments before kickoff at the Tottenham Hotspur Stadium.
Pep Guardiola was questioned about Akanji's fitness at his post-match press conference, and told reporters: "In the last action, felt something in the muscular part of his body and today in the warm-up he didn't feel good. He said 'No I can take a risk', and I said, 'No, no risk!'"
Akanji has been a first-team regular under Guardiola so far this season, starting 12 of the Citizens' 15 matches across all competitions.
The 29-year-old's omission from the starting lineup in midweek has since sparked concerns that he could miss Saturday's Premier League clash away against Bournemouth.
Akanji could be fit to play against Bournemouth
However, Akanji appears to have reassured Man City supporters that he has not sustained a serious issue and could be involved in some capacity at the Vitality Stadium.
Indeed, speaking to Sky Sports reporter Anton Toloui, Akanji is said to have revealed that he is 'hoping to be back in training on Friday and ready for Bournemouth on Saturday'.
It was initially reported that Akanji had sustained a calf issue in the pre-match warm-up on Wednesday, but the defender is said to have instead felt 'tightness in his groin'.
The news about Akanji's fitness comes as a huge boost for Man City at a time when they could have as many as eight other players missing this weekend's clash with Bournemouth.
Savinho was taken off on a stretcher with an ankle injury in the second half of the defeat to Spurs, while Josko Gvardiol picked up a knock at the end of the game, and both players will be assessed ahead of kickoff.
Meanwhile, Premier League leaders Man City are still having to cope without Rodri (ACL), Oscar Bobb (leg fracture) Kevin De Bruyne (groin), Kyle Walker (knee), Jeremy Doku, Jack Grealish (both unspecified) due to injury.
Guardiola will provide a fresh update on the fitness of his Citizens squad at a pre-match press conference on Friday.