McClean, who was on the verge of a move to Darren Ferguson's side before signing for Sunderland, is eager to to make his second consecutive start and his first in the FA Cup after scoring against Wigan last week.
"[Peterborough] had a bid accepted," he told the club's official website. "I went and met the manager and things like that, but it didn't materialize for one reason or another.
"I'm just looking forward to progressing here and not focusing on what could have been. We have got to show Peterborough a lot of respect. It's going to be a tricky game, especially at their place.
"Peterborough score a lot of goals so it should make for an entertaining game."
McClean, 22, has made five appearances since arrival at the Stadium of Light for £350,000.