The former West Ham boss is a member of the FA board responsible for deciding on who will lead the national team at Euro 2012.
And, whilst the 63-year-old was quick to assure fans that the Three Lions are in a good position ahead of the tournament, he admitted that there may not be an appointment any time soon.
Brooking said: "Everything will be in place, the backroom staff is very good. Whoever comes in will be really happy with that.
"The issue is the timing, that is why we don't think we are in any rush.
"I think you could get somebody parachuted in a few days before it, though I'm sure there are some people in our group who don't want that."
Tottenham coach Harry Redknapp is the bookies' favourite for the role, which is currently being filled by caretaker boss Stuart Pearce.
Brooking added: "We've been concentrating on the Holland game. Now we'll sit down in the next few days and see what the timeframe is.
"We will take our time. I don't see anything happening soon. We obviously want to be aware of all the sensitivities before taking it forward. There are sensitivities."