"I am sure he would do a very good job if he stayed on but it is unfair to put that pressure on him. He is his own man and he has said that he doesn't particularly want it, so we will see who comes in."
Brooking will be involved in selecting the new man, although he will be in Macedonia over the weekend working for the BBC.
West Ham, who have made a promising start, are desperate to return to the Premiership at the first attempt and could therefore target a manager who has had experience, and achieved success, in the lower divisions.
Reading's Alan Pardew and Nottingham Forest boss Paul Hart are both building impressive reputations in Division One - and Gary Megson has already experienced promotion with West Brom.
Brighton manager Steve Coppell also has a good record outside the Premiership and Oldham's Iain Dowie was an early front runner with the bookmakers.