Messi had a knock in PSG's win over Lyon as MRI scan earlier this week confirmed signs of a bone contusion.
Pochettino who is waiting for the return of the Argentine forward also disclosed the six-time Ballon d'Or winner will be assessed for further update.
"Messi has started to run today. We are going to assess him and we hope he improves," Pochettino told reporters on Friday.
"Let's wait for him to come back, but in any case we have to be cautious and in the next days we will see his progress.
"On Sunday, we will be able to give a positive update. We hope everything goes well and he will be available again. Yes, we hope he can play (against City). We have to be cautious."
With Angel Di Maria still serving his suspension in the Champions League, Pochettino insists that won't affect his selection on Saturday against Montpellier.
"We will see, there are different options and different systems. We will see who gives the team the right balance. We also have the flexibility to change as we go," Pochettino added.
"Mauro Icardi is a player who contributed a lot up until his injury. He then recovered and has made a big impact. Of course, he offers us an alternative in our attack."
Messi completed his shocking move to Paris Saint-Germain on a two-year deal with the option of extending for a further year after departing Barcelona.
Bringing to an end of a 21-year stay at Barcelona, Messi remains the club's record scorer with 672 goals and won 10 La Liga titles, four Champions Leagues, seven Copa del Rey trophies, including six Ballon d'Or glories.
