Reports have suggested Liverpool are weighing up a move for O'Neill if Rafa Benitez departs Anfield this season.
Benitez's future at Liverpool looks uncertain after a disappointing campaign with Italian giants Juventus believed to be keen on luring the Spaniard to Turin.
O'Neill's own position at Villa was speculated about earlier this season, but Lerner revealed earlier this week that the Northern Irishman was staying put after talks between the pair.
Lerner, who took control of Villa in 2006, is keen to keep hold of O'Neill and has told Liverpool they would be wasting their time if they made an approach for the former Celtic and Leicester chief.
"I don't want a manager who nobody else wants. But, as far as I'm concerned, Liverpool are not taking Martin O'Neill away from Aston Villa," Lerner told the Daily Star on Sunday.
There have been reports of an uneasy relationship between Lerner and O'Neill, but the American insists he is happy with O'Neill's character.
"If you look at the top managers, you realise you are dealing with animated, complicated people," added Lerner.
"With Martin you've got a lot of personality, a lot of points of view, a lot of history and a lot of stuff going on. I realise that's who my manager is.
"And I don't want anything different than what I have here now."
Lerner also revealed he will not be splashing out big money on players this summer saying the club cannot afford to spend £30million on one star.
"I tell the truth. To anybody who asks me, I will simply say that I cannot afford it.
"It isn't that I'm not prepared to write the cheque. But we have tried to build the club in a steady, reasonable way. And £30m players are not a part of that.
"You also have to consider what you would pay the player and what the other players would think about it.
"It would just not be at all consistent with anything that we have done since I've been at the club."