"There's many managers out there who obviously will want the job," said Beckham, who is in Australia for Los Angeles Galaxy's exhibition match against A-League club Sydney FC on Tuesday night.
"It might be a tough job, it might be a high pressure job to manage England, but any manager in football would love to manage our country and our players.
"Luckily enough I'm not in a position where I have to choose and pick the manager for our country because I think it's going to be a very tough decision.
"It's going to be a tough decision for whoever's going to make it at the FA but I'm not going to sit up here and name names because there are so many thrown in already.
"We'll just have to wait and see."