The Scottish defender has been struggling with an ankle problem during pre-season and has been forced under the knife in a bid to have him fit for the majority of the campaign.
"Phil Bardsley has had an operation," O'Neill said on the club's official website. "That's a real blow for us.
"Stephane has done a little bit of training this morning, and hasn't felt any effects.
"He hasn't been able to do that much but in the course of the next few weeks in terms of the sort of fitness level that he can attain, we hope he gets there pretty quickly.
"Wes Brown is feeling a bit better but obviously getting a bit annoyed that injuries have plagued him.
"David Vaughan's making progress and he had an operation on his side to cure a problem and he's making good progress out there on the training field, but hasn't joined in with us yet."