The Bulgaria international has urged Villa to try and match the ambitions of Milner, who has been the subject of speculation linking him with a move to Manchester United.
The 24-year-old is halfway through a four-year deal and is due to have talks over a new contract in the summer.
Villa went through a similar scenario with one of their top stars 12 months ago, when Gareth Barry moved to Manchester City after 12 seasons at Villa Park.
But the midlands club have taken further strides forward this season under manager Martin O'Neill and are still in contention for a Champions League spot after Sunday's win over Birmingham.
Petrov said: "There are a lot of players at this club performing at a high level so there's going to be speculation. They are very good, young talented players with big futures.
"If the club wants to go forward, we need to keep our best players like any big team - Manchester United, Arsenal, Chelsea and Liverpool.
"They've tried to hold onto their best players and I hope our chairman and manager will do their best to keep our good players as well."
Petrov added: "It is very important we keep James. We have got a lot of talent at this club which has cost a lot of money. We need to make sure they are happy and stay here.
"He's been enjoying his football and that's the main thing for a player.
"If we try to match his ambition, and the club show they are doing things the right way, I don't think James will go somewhere else.
"People say that if Manchester United coming knocking at your door, it's a different question, that the manager and the player then need to make a decision.
"James can play in any team and at that level but we hope he will stay with us."
Villa have taken 13 points from five games since the 7-1 mauling at Chelsea appeared to have ended their chances of a top-four finish.
But Petrov is adamant that Villa have never given up hope of achieving that goal.
He said: "I remarked four or five weeks ago, when people were writing us off, that there would be plenty of twists and turns and that's what happened.
"Fair play to Tottenham, they took their chances in two games that many people didn't expect them to win (against Arsenal and Chelsea).
"We're still in the mix and it's up to us now. We'll probably have to wait for other teams to drop points but it's up to us to try and win our games.
"We're going in the right direction and we'll see what happens at the end of the season.
"It's been a great season with the two cup runs and we've said all along that we wanted to make sure such a great season didn't end with us having nothing to show for our efforts."