Delaney, now an academy coach at the club, said: "Martin O'Neill knows Liverpool are a bigger club than Villa.
"It hurts me to say that as a Villa supporter through-and-through and the club mean a hell of a lot to me. If Martin didn't say he would have done the same as a player, he would be lying. Anyone would.
Delaney claims Barry would be "crazy" not to go because he might not get another chance to play for a Big Four club.
The Welshman cannot see Villa qualifying for the Champions League and says Liverpool represent Barry's best chance of winning trophies.
"Gareth has been as loyal as any Villa player," he said. "The thing is, I can't see them breaking into the top four in his time.
"They exceeded all expectations last season, but can they do it again? I don't know.
"Gareth will be 28 in February. If he goes, he will win trophies. If he doesn't go, it will be crazy for his career.
"He has to give it a go. If he can't go the opportunity may never arise again. Liverpool might not ask again. He has to grasp this with both hands. The choice is Champions League and England with Liverpool or the InterToto with Villa.
"(Villa owner) Randy Lerner could probably match what Liverpool can offer Gareth in terms of wages, but this is not about money. He loves Aston Villa, as I do, but for his career, this is the right move."