Former Liverpool manager Gerard Houllier is now among the bookies' favourites behind Sam Allardyce to replace Keane as the Sunderland chairman, Niall Quinn, sifts through the applications.
The uncertainty has left Ferdinand under no illusions about what is ahead. "As fast as you've come in the door, you can leave just as quickly," he said. "But the boys have got a lot of pride in themselves, which we showed at the weekend against Manchester United.
"None of the boys want to give up that shirt, none of the boys want to leave the club. If they wanted to, their attitude wouldn't have been spot-on at the weekend."
Keane's successor will inherit an over-populated senior squad thanks to the Irishman's transfer policies, but Ferdinand showed he is ready to rise to the challenge of proving his worth with an impressive display during the 1-0 defeat at Old Trafford.
"It's not always down to the manager, it's down to the players," Ferdinand, 23, added. "We've got to stick together now more than ever, whether there's a manager here or not.
First-team coach Ricky Sbragia is due to remain in charge when West Bromwich Albion head to the Stadium of Light on Saturday and there is even talk that he will be at the helm when Sunderland head to Hull a week later.
Keane's former United colleague, Dwight Yorke, who is assisting Sbragia, has pledged not to follow Keane through the exit door.
"They need a bit of stability in there," Yorke, 37, said. "It's good to be playing again and good to be involved.
"I'm very grateful for the fact he [Keane] brought me to the club but at the same time I'm very sad to see him go. I genuinely believe he could have turned things round, but for whatever reason he decided not to."
Meanwhile, Sbragia has hit back at Gary Neville after the Manchester United captain labelled his tactics "appalling".
"We had all these plans about going forward but they pinned us back and we couldn't get out," the Sunderland caretaker manager said.
"What I didn't want was to play open football and lose 6-0. I wanted to frustrate them and hit them on the counter-attack, but United pinned us back. We tried to get out but we found it very difficult. Our forward play was virtually non-existent.