Villa skipper Petrov hopes that Villa can retain the services of Downing and bids of £12million and £15million from Liverpool have already been rejected.
But the Bulgaria international has faith in McLeish to ensure Villa remain competitive in the Premier League, even if Downing follows Ashley Young out of the door.
He said: "We'd love to keep Stewart. He was exceptional last season and is a great talent.
"That's why he was voted the fans' player of the year and players' player of the year and he deserved both awards. He works really hard and, like I said, he's an exceptional talent.
"But the chairman (Randy Lerner) is the man who knows what is right and wrong for the club and he will always do what is right for the club and so will the manager."
Petrov added: "Ashley Young has moved on, so have Gareth Barry and James Milner in recent seasons but as a club we will keep fighting.
"That's why the chairman brought in a manager with a fighting spirit.
"He will make sure we have a strong, competitive team that will be able to compete against other big teams in the Premier League. That's why he's been appointed.
"It's not nice to see good players go but that's the way football goes.
"We're not going to stop fighting, we're professionals and we're going to try to win as many games as we can to climb the table as high as we can."
Petrov believes McLeish is the right man to revive the club's fortunes but pleaded for him to be given time to make his mark.
McLeish met the Villa players en bloc for the first time on Friday when they reported back for pre-season training.
Petrov knows all about his new boss from when he was playing for Celtic and McLeish was is charge of Old Firm rivals Rangers, and has no doubt about his quality.
He said: "I met the new manager a few days ago but I know him from before also and I'm really glad we have someone like him in charge of our team.
"He's a man who is a bad loser, he likes to win and he likes to be on top of everybody. I think we need a man like this.
"The chairman is aware of his ability and what he can do and I think he's the right choice of person to lead this club.
"He needs to be given time. Everyone deserves time and he'll prove to be the right man for this job, no question. He's got that will to win."