O'Neill has been rumoured to be wanting out of the club following reports of a row regarding his transfer budget and he will be meeting with owner Randy Lerner at the end of the season.
The former Celtic and Leicester boss took over at Villa Park in 2006 and has overseen his side's rise into challenging for a Champions League place over the previous two campaigns.
Lerner's right-hand man Charles Krulak has insisted that there has been no deterioration in the relationship with O'Neill, and Petrov is hopeful that his boss will stay at the club beyond the summer and not be tempted by other big clubs.
"I'm sure the manager is not short of propositions from other clubs - but we all want him to stay as he has done a great job here and he's a great man as well," said Petrov.
"Hopefully, after the summer meeting, he will still be here."
Despite the denial of a rift between the pair, Petrov hopes that O'Neill and Lerner will enjoy a positive discussion in the summer and solve any issues they may have.
"He has certainly got his own view about things - and those are between the manager and chairman," he added.
"The most important thing is how they solve these things - and keep it together.
"They are both grown men and I'm sure they will get things together."
The Bulgarian also had some strong words for Chelsea captain John Terry, who he will march out alongside at Wembley in their FA Cup semi final next week.
Terry spoke out after his side's 7-1 mauling of Villa last week about their tendency to 'tire after 60 minutes', something Petrov found to be disrespectful and warned that there will be no repeat of.
"It's very easy for somebody to go and make comments like that when they have beaten you 7-1. But I didn't see him making them after they lost 2-1 at our place," Petrov said.
"And I can promise our fans they have nothing to be scared of at Wembley.
"Both the performance and result will be different."