O'Neill insisted the Reds have made a player exchange offer for 27-year-old Barry, who has two years left of his current contract.
Goalkeeper Scott Carson, currently on loan at Villa, and defender John Arne Riise could also come into the equation if a cash-plus-players deal materialises.
O'Neill told Villa's website: "Gareth Barry still has two years of his contract left to run and from my two years' experience of working with him, he's not one who would be wanting to break contracts lightly.
"Liverpool haven't made a straight cash offer. They have made an offer involving a mish-mash of nameless player exchanges.
"I'm particularly disappointed to hear that business is being conducted in public and I just want to be clear on this in that we're trying to build a side here and we're not a feeder club.
"We want to be trying to challenge. At some stage we want to get to the position that this football club once held. That will demand an awful lot of effort. It will take a supreme effort and it will take very, very good players."
O'Neill added: "I don't want to be in a position of letting really good players go. Gareth Barry is a really good player who still has two years left on his contract.
"I haven't discussed these things with him yet. At some stage obviously I will do. But the day before probably our most important game of the season is not the time to be discussing it.
"A couple of weeks ago Gareth said he would prefer to wait until the end of the season before we start discussing things and I think that would be the right thing to do.
"It's particularly disappointing to find out that Liverpool have carried the story in their local paper. It's certainly not the way that the Liverpool of old conducted business. I prefer to do things with a bit or privacy and a bit of confidentiality.
"That's particularly disappointing, especially at this time.
"We've got two important games coming up. Liverpool's season might effectively be over as they have qualified for the Champions League and their interest in this season's Champions League ended a couple of nights ago.
"I'd rather be waiting until the end of the season before I discussed things."