MacDonald took over as caretaker manager after O'Neill's shock resignation and he made the perfect start with Saturday's 3-0 destruction of West Ham.
The Scot, who briefly held the caretaker role at Leicester in 1994 before following Brian Little to Villa, has said he is not a big enough name for the job.
But Lerner suggested MacDonald is in the running, having given him the green light to stay in charge for Thursday's Europa League tie with Rapid Vienna.
And Petrov, who scored Villa's second goal in a commanding opening-day performance against the hapless Hammers, revealed the players are right behind him.
"The way he prepared us for the game showed us that he wants to hold onto that job – and I hope we can help him take that job," said Petrov.
"We are behind him. He has been at the club a long time, done a great job with the youth and he has the opportunity to do it now."
Lerner revealed he will wait to be guided on the managerial decision by MacDonald's own view of the situation.
"There are those managers who like the show and the attention – and then there are those such as Kevin," he said.
"I'm not going to say it is in Kevin's hands now but much will depend on how Kevin feels, whether he thinks this might be right for him, if he is comfortable with the idea of being Villa's manager."
Marc Albrighton, newly-capped England Under-21 winger, had a major hand in all three Villa goals. Stuart Downing finished the first from close range, Petrov headed in the second and James Milner wrapped up the victory in style in what could be his final game for the club.
Former Leeds United midfielder Milner's name was jeered before kick-off but he left the field to a standing ovation, although MacDonald was not confident the England international would still be around for the Vienna trip.
Manchester City are in negotiations over a deal for Milner which could see Stephen Ireland move in the opposite direction.
"The latest I heard, there was still a stalemate with Man City but that could change within hours," MacDonald said after the game.
Just as Villa put the managerial upheaval to one side, so Milner refused to be fazed by all the transfer speculation swirling around his head.
Petrov said: "He is giving everything for the club like he always does. He's a great pro and people should learn from him."