Bulgaria meet Belgium in an international friendly on Wednesday, a week after Manchester United striker Berbatov announced he was quitting the national team.
"He deserves to be the team captain but I'll have to talk to him to reconsider his decision to not talk to Bulgarian media," Stoilov said of Petrov.
The Aston Villa midfielder, who quit the national team in 2006 after a row with former coach Hristo Stoichkov but returned only five months later, has refused to speak with local media in recent years after receiving some strong criticism.
"It's important to have a good communication between the national team, the media and the fans and I think Stilian will realise that importance," Stoilov told a news conference on Monday.
The absence of Berbatov, Bulgaria's all-time leading scorer with 48 international goals, will be keenly felt, Stoilov said.
"It's our responsibility to try to compensate for Berbatov in the best possible way.
"Obviously, it'll be difficult because he was one of our leading players and we've been heavily dependent on him for materialising the scoring chances.
"With Berbatov missing we'll try some new things in attack. I want to see an improvement from (Parma striker) Valeri Bojinov. Bulgaria expects a lot from him, I expect too..."
Bulgaria failed to qualify for the 2010 World Cup and have been paired with England, Switzerland, Wales and Montenegro in Euro 2012 qualifying.
"We really hope that some of our younger players will grab their chance but I require a lot more of them," said Stoilov.
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