The Manchester United striker, who is the second-most capped player in the current set-up behind Frank Lampard, is the favourite to inherit the armband after Gerrard announced his international retirement this week
Former England midfielder Wilkins would put Rooney on his shortlist, alongside Manchester City's Joe Hart and Chelsea's Gary Cahill, but would opt for go for the striker because he says he possesses all of the required attributes.
He told Sky Sports News: “They need a player who can actually worry about other people and be quite confident with their own game.
“To lead a group of players, even if your game is going drastically wrong, you have to be able to see stuff as far as your team-mates are concerned and to be able to get around them and give them some assistance as well.
“I think Rooney is more than capable of doing that. I think he’s been very fortunate that he’s played under a lot of very, very good and influential players at Old Trafford so it stands him in good stead.
“Rooney, [Gary] Cahill and [Joe] Hart would be, for me, the only three that could actually guarantee their places in the England side. They have to be the top three candidates.
“[Rooney] is the standout candidate, I think the bookies have got it spot on."
Wilkins also stressed the importance of England’s next captain having a settled lifestyle with guaranteed playing time at their club.
And he suggested that Arsenal midfielder Jack Wilshere, who was photographed smoking in the newspapers recently, would not fall into that category.
“A lot of the stuff off the field has to be handled in the right way,” Wilkins continued.
“To be England captain you’ve got to be a pretty stand-up person.
“As good and as talented as Jack is, I don’t know whether he’s going to be a starter at Arsenal this year with the players they have. And there’s a number of players on that list, as well, that find themselves in a very similar situation.”