Everton parted company with Ronald Koeman after a disastrous opening to the campaign, and they are now taking their time to assess their next option.
The Toffees have had David Unsworth in charge for their last two matches, and the caretaker boss has expressed a desire to take the job on a full-time basis.
However, Unsworth has lost both his games in charge since taking over from Koeman and it is likely that he will need a result in the near future if he is to land the job.
Everton’s next two matches come against Lyon in the Europa League and Watford at the weekend.
And Redknapp insists that whoever Everton appoint, they must stick by him, regardless of what happens during the early stages of his leadership.
“It’ll be a tough game tonight,” Redknapp said. “Unsy’s a great lad and he’s done a fabulous job, but I don’t know [if he’ll get the job]. Theres a few people around that would fancy that job. He needs two good results, and if he doesn’t it’ll be difficult for him.
“They need someone to take the club forward. We all know Everton is a great club and the tradition of the club is amazing. It’s a club which should be going forward, everything is in place there.
“They can’t have a couple of bad results and panic again, they need someone for the long-term to take them forward.”
Whoever takes over at Everton has a huge job on their hands, as the Toffees are currently locked in a relegation fight.
Everton are sat in 18th place in the Premier League table, with concerns mounting at Goodison Park.