MacDonald took over as caretaker manager after O'Neill's shock resignation and he made the perfect start with a 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 clash 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.
"I said to him before the game, 'you try and hold onto that job'.
"He knows it's hard. Expectations are high and people want success and they talk about big names - but he has the opportunity and he is really determined to stay there.
"We played really well, we showed what we can do and if it keeps going that way there is no reason why he cannot make his own name."
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.
"He is such a cool guy, he is popular with the players who really played for him and with the fans and the press. We will see how he feels when he wakes up from this and then we will look at the situation from there."
MacDonald has held a number of posts at Villa, most recently as reserve-team coach. He awarded a first Premier League start to Marc Albrighton, the newly-capped England Under-21 winger, and it proved to be an inspired selection.
Albrighton had a major hand in all three Villa goals. 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.
West Ham could not live with Ashley Young's pace and movement, while Albrighton led Herita Ilunga a merry dance down the right wing all afternoon. On the other flank, Downing was in a different league to West Ham's Kiwi debutant Winston Reid.
Petrov continued: "Every manager has a different style and Kev has a different vision on how we can play and we showed today we can be faster and play with more freedom.
"He always believes that the young players coming in are the future of the club and he's been working with these kids for a long time.
"He (Albrighton) played like it was his 100th Premier League game. He was quick and confident and he tried to beat people and create chances for us. He did really well."
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: "When you are a good player and teams want to pay £20million, £30million for you then you can do nothing about it.
"He is giving everything for he club like he always does. He's a great pro and people should learn from him.
"He deserves the standing ovation because you don't see many more honest players in the world coming out and playing like that with such heart.
"He was flattered by the reaction - and when you make the fans happy and see them behind you, it makes it even harder to leave.
"After Saturday he may even decide to stay."