Milner has two years left on his contract and has attracted interest from several clubs, but Lerner intends to hold on to the winner of the Professional Footballers' Association young player of the year award.
"I am not worried about losing James Milner and I think he will play for Aston Villa," said Lerner.
"I'm not dismissive of the realities of the situation whereby a player who has received the attention and acclaim of James Milner is going to spark discussion and debate about whether or not he will move.
"But I don't worry about him leaving because he is wanted at this club. We will do everything in our power to keep him."
O'Neill met with Lerner on Tuesday to discuss Villa's season and their plans for next term.
"Martin will be back next year managing," added Lerner.
"It has already been settled. He and I spoke on a number of occasions in person and over the phone. Yesterday [Tuesday] I dragged him out of a series of meetings with chief executive Paul Faulkner trying to get plans for the summer underway.
"We feel very good about that because it represents continuity for the players and in many other ways."
Villa finished sixth in the Premier League to qualify for next season's Europa League and also reached the final of the Carling Cup and semi-finals of the FA Cup.
Although they fell short in their bid to break into the Premier League's top four and reach the Champions League, O'Neill was delighted with his side's overall campaign and is now hoping that he can push on next season after summer strengthening.
O'Neill admitted last week that he would need to improve the team just to stand still in a fiercely competitive top flight.
A £30m striker would be out of our budget but there is money there to be spent on the team
Lerner confirmed that some funds would be available for O'Neill to strengthen his squad during the summer although he admitted the club would not be able to sign a £30m player.
"I gave Martin the assurance that I also wanted to take the team forward," said Lerner.
"A £30m striker would be out of our budget but there is money there to be spent on the team.
"I say that carefully in the context of knowing that the summer brings a very dynamic environment of players coming and going so I'm careful not to simply say 'here is a brand new amount of money, go and spend it'.
"I would prefer to say our ambition remains to get better and we are not in some sort of mode where we are shutting the door on spending on players.
"Is there a sell to buy policy? I think there is a sell to buy policy in every organisation on the planet.
"On the other hand if an opportunity arises and the net 'sell to buy' doesn't equal what is required to take advantage of an opportunity, then you may spend the money. I wouldn't exclude us from the group who would do that."
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