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.
"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..."
"We really hope that some of our younger players will grab their chance but I require a lot more of them," said Stoilov.
