Villa have been without a permanent boss since the eve of the new season when Martin O'Neil quit as boss.
Kevin MacDonald was appointed on a caretaker basis, but was overlooked for the job as Houllier was handed a three-year deal.
But Villa are being forced to wait for Houllier, as he looks to finalise his release from the France Football Federation, where he is the technical director.
And Petrov admits that the sooner Houllier arrives, the better it will be for the club.
"It is complicated," he told the Daily Mirror.
"Complicated for the new manager, complicated for Kev as well, but we will see the new manager soon.
"We wait to see how we can improve and we look forward to stability."
The Bulgarian is also looking forward to working with the former Liverpool boss.
"He has been at the top level for a long time," he said.
"He managed Liverpool, had success, been manager of Lyon. He knows what he needs to do.
"We try to do our best for Kev because he has been at this club for a long time and has done a tremendous job."