The Spanish midfielder picked up a hamstring strain that was anticipated to keep him out of the match while on international duty last week.
However, Citizens assistant boss Brian Kidd has revealed that the 26-year-old could make his comeback against the Dutch title holders after making a quicker than expected recovery.
"We're having a roll call today (Monday), with scans and everything. With David in particular, we don't know how long he will be out for," assistant manager Brian Kidd told the Manchester Evening News.
"I think they are looking at him thinking he might be in with a chance of playing on Wednesday against Ajax. With a couple of days for it to settle down, we will get a better picture."
Silva joined City from Valencia in 2011 for a reported £24m fee.