Roberto Martinez was sacked as the Everton manager on Thursday afternoon following a disappointing season for his side.
They are currently 12th in the table, and were beaten comfortably by Sunderland at the Stadium of Light on Wednesday.
The season will be the second successive they have finished outside of the top ten, a position far below where many believe a team of their ability should be.
It has cost Martinez his job, and Cottee says his personal favourite to replace him would be Eddie Howe, but Frank de Boer will be the overall favourite.
“It’ s a big job but it’s also a fantastic job as it’s an incredible football club,” he told Sky Sports News.
“Frank De Boer will be one of the favourites going forward, Ronald Koeman, the fans would love to see him but I cant see him leaving Southampton and Mark Hughes is another one.”
“My personal favourite would be Eddie Howe, but prising him away from Bournemouth isn’t going to be easy. It’s a tough job for the new owner.”
It will certainly be interesting to see who Everton appoint as their next manager given the names that have already been linked.
One name Cottee does give is departing Manchester City manager Manuel Pellegrini, who is leaving the club this summer.
Given his history of managing big clubs, namely Real Madrid, then will surely also be among those the club looks to interview.