Interim head coach Stephen Frail is not in the frame and may even lose his job on the backroom staff.
Fedotovas, who was in Edinburgh for the club's AGM, told HeartsTV: "I agree that the managerial position was not ideal. We are working on the issue and we are speaking to potential candidates.
"We will not go for easy decisions and a quick appointment just to please fans in the short term.
"Some supporters really want to see a British-style manager but I also agree with people who say we need a skilful manager, that doesn't depend on his nationality.
"I'm more than convinced that both British-style and European-style managers can work in this environment if they are intelligent enough.
"I believe a new manager will be coming on board, if we are lucky, for the start of the new season.
"From the end of the season to the start of the pre-season training hopefully, we are working in order to meet that timing."
Frail's long-term future with the club is in the hands of the new manager.
"My understanding is that he will not be in a long-term position with the club," Fedotovas said.
"We are really grateful to him for what he is doing. He can work alongside the manager but this is up to the people who will be coming to the club to decide. But we will really support him."
The Lithuanian also revealed that majority shareholder Vladimir Romanov will continue to have his say on new signings.