City manager Roberto Mancini had originally targeted the club's next Premier League match against Swansea City for the Spain international's comeback but assistant Brian Kidd has revealed that he could play even sooner.
Silva will undergo treatment on his hamstring problem on Monday ahead of the match against the Dutch champions in Amsterdam. He sustained the injury while playing for his country against France during last week's international break.
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"We're having a roll call today, with scans and everything," Kidd told the Manchester Evening News. "With David Silva in particular, we don't know how long he will be out for.
"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."
Defender Maicon and midfielder Javi Garcia are also fitness doubts for the club's third group stage contest of the season but Kidd hopes that the duo's recovery can be stepped up this week.
"Javi Garcia and Maicon are there or thereabouts," he added. "They have done a little bit of training but haven't done everything yet - they are back in today and we are hoping the next couple days will bring them on."