Wayne Rooney says it would be "better" for a homegrown manager to be the next England boss, but admits it is all about getting the right man for the job.
Two of the country's last four permanent bosses have been foreigners - Sweden's Sven-Goran Eriksson and Italy's Fabio Capello - and Football Association chief executive Martin Glenn suggested on Tuesday nationality would be no barrier for the right candidate.
Roy Hodgson revealed on Monday night he was resigning following England's 2-1 loss to Iceland in the last 16 at Euro 2016 in Nice.
Rooney, who played under both Eriksson and Capello for the national side, claims whoever the new man is will be inheriting an exciting squad, despite another disappointing summer campaign.
When asked for his opinion, Rooney said: "Of course, it's better if he's English, but he has to be the right man for the job. He has to have the credentials and the ability to be able to do the job. Whether he's English or not, we'll wait and see.
"He needs to put his stamp on the team, whoever he is. I know one thing, if I was the manager coming in, I'd be very excited. It's difficult to see now, but we do have a good squad, an exciting squad.
"Whoever comes in will have a tough job, but they have the players to move us on from where we are and take us one step further."
Goalkeeper Joe Hart was less committal, insisting he had not yet considered the vacancy.
"I haven't even given it a thought, the next manager," he said. "I've been that involved in what we've been doing here. It's not an easy job anyway, the England job. We win and lose as a group and we've enjoyed working under Roy. Obviously none of us wanted these to be the circumstances in which he left his job. It's difficult.
"I'm sure whoever gets the job will deserve it but, living in the now, and trying to deal with what's gone on, we're going to have to deal with it as a group - players and coaches - and deal with it as best we can."
Hart, whose starting spot is coming under question after two high-profile errors in France, has seen England falter on the big stage before and seemed bereft of solutions for the side's repeated under-achievement.
"It's tough to say because obviously I've been part of some pretty bad campaigns. We're going to have to switch it up, get better," he said.
"It's difficult to come out and be positive, to say positive things, after what happened. Ultimately we failed and we're going to have to deal with it. The wounds are fresh, that's for definite."