McGeady was forced to undergo a prolonged period of rest after playing through a broken bone in his foot towards the end of last season.
As such, he missed the opening part of Sunderland’s pre-season schedule.
However, the Irishman has been in Portugal with the squad and delighted Jack Ross with the progress he has made.
He now has an outside chance of featuring in the Black Cats’ third pre-season fixture.
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Either way, his progress is greatly encouraging just a week after he committed his future to the club.
Last year he had no pre-season at all, thrown straight into action in September and going on to have a hugely successful campaign.
“Aiden has got an outside chance of maybe playing a little bit of the game at the end,” Ross said.
“He's getting a little bit more training than we'd imagined here, he looks good and feels good, it has been positive so far.
“We'll see how the next couple of days go but there's a chance, whether it's just the very last part of the game, which would be ahead of schedule to what we'd imagined.”
Ross also revealed that Max Power is ahead of schedule as he recovers from an ankle problem.
Though he remains a doubt for the season opener against Oxford United, Power has been in Portugal.
Ross said: “Max is ahead of schedule as well, a little bit behind Aiden but further ahead than what we thought which is positive.”