Brooking is one of four men charged with the task of finding Fabio Capello's successor after the Italian stepped down from the role.
Stuart Pearce took temporary charge of the midweek friendly against the World Cup runners-up and, on Thursday, admitted he is not in line for the permanent position.
Pearce is keen to lead the national side for the European Championships in the summer, while Tottenham Hotspur manager Harry Redknapp remains the overwhelming favourite to take the reigns in the long-term.
However, with Spurs looking to secure a top-three finish in the Premier League and an automatic passage to the Champions League, the national side's managerial position could remain vacant for some time.
But Brooking is not worried about the possibility, insisting thorough preparations are being made for the tournament in Poland and Ukraine.
"Everything will be in place," he is quoted by The Independent. "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."
The Director of Football Development with the Football Association has confirmed that the hunt for a new manager had been put on the back-burner ahead of the Dutch game.
"We've been concentrating on the Holland game," he said. "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."
'Will Cristiano Ronaldo and Neymar extend their contracts in Saudi Arabia? We play a facilitating job, but it’s down to the players and the clubs to decide' Saudi Pro League chief reveals how talks will work for out-of-contract duo
Nations League: Who are the ITV commentators and pundits for England vs Republic of Ireland?
