O'Leary worked with Robinson when in charge of Leeds and then tried to sign him from the Whites when manager of Villa five years ago.
O'Leary said: "I have spoken to Paul briefly and gave him my opinion on Villa just as I did when I first tried to sign him.
"It would be wrong of me to say whether I know he's going to Villa or not this summer but I told him it is a massive club with big support.
"There's a real chance for him to do well there. I told him he should sign this time if he gets the opportunity especially as the club seems to be in good hands and making progress.
"Paul was desperate to come to Villa five years ago and I'm sure that hasn't changed.
"When I tried to sign Paul before, he was asked to take a pay cut which he didn't want to do.
"The terms of the deal just weren't right for him and it was difficult for me because I knew Paul from Leeds.
"But he would have been a bargain and at the time I said then he would be Villa's goalkeeper for many years to come if we could have got him.
"In the end he went to Spurs but I still think he's got a good few years ahead of him at Villa.
"I honestly think he would be a great goalkeeper for Villa."