The FA are set to start the search for Stuart Pearce's successor after it was announced that his contract would not be renewed at the end of the month.
Former Middlesbrough manager Southgate was installed as the early favourite with the bookmakers after previously working for the FA in a role as head of elite development and Sky Sports pundit Wilkins says he would be a sound appointment.
But he also sang the praises of recently retired Everton defender Neville and former full England boss Hoddle, who was named as the second favourite in the early markets.
Wilkins told Sky Sports News HD: "When you look at Glenn Hoddle's win ratio for the national side, it was something like 61%.
"He had a good crop of guys coming through and he utilised them in the best possible fashion. I think Glenn would be a great choice.
"Gareth Southgate would be a fabulous choice as well because he's closely associated with the FA.
"I think Phil Neville would be a good choice because he's worked under a lot of fantastic coaches so should have a terrific knowledge of our game.
"He's a young man and understands a little bit more the psyche of the younger player coming through.
"I certainly think the top two in the betting and Phil Neville would probably be my choices."
Wilkins says that whoever gets the job must seek assurances from the FA that the best players will be made available to the Under-21 squad.
High-profile players such as Jack Wilshere and Phil Jones did not travel to Israel for England's disastrous European Championship campaign and Wilkins says that may have cost Pearce his job.
He added: "The only thing the FA should dictate to clubs is the fact that if the next manager chooses and selects a player then he will be there, no two ways about it.
"We've got the same situation with the first team. They have to be there to say that they're injured.
"I feel sorry for Stuart because I don't think in any finals he's ever taken part in has he had his best group of players. I feel sorry for him because the rest of the top nations will put their top players forward and they will play.
"If you're selected to play for your country, that's the ultimate you can be no matter what level you play at. I think our problem is some of our lads think when they get in the full squad the Under-21's is almost below them.
"That's not the score. I'm sorry, but if you're selected to play then go and play and do the best that you possibly can because I think Stuart's hands have been tied behind his back."