The 32-year-old has been on the sidelines since the end of June following knee surgery, missing City's final eight Premier League matches of the season, in addition to their Champions League last-16 second leg against Real Madrid.
Aguero is currently in Barcelona working on his recovery alongside surgeon Dr Ramon Cugat, though, and it is thought that the Argentina international has a chance of playing a role in the latter stages of the tournament.
The Citizens will take on Lyon in the quarter-finals of the competition on Saturday night before a potential semi-final against either Barcelona or Bayern Munich on August 19.
"Sergio will be given as long as possible to recover – and the fact that he is still working on his fitness rather than being told to step down is because he still has a chance," The Mirror quotes a City insider as saying.
Aguero has been in strong form for Pep Guardiola's side this season despite his injury problems, scoring 23 times in 32 appearances in all competitions, including two in three Champions League outings. body check tags ::