Steven Gerrard stood down from the post on Monday after 114 appearances for his country and Robson, who scored 26 goals in 90 internationals, believes Rooney is the ideal choice in the absence of any stand-out names.
Speaking to Sky Sports News, Robson, who skippered United for 12 of the 13 years he spent at Old Trafford between 1981-1994, said: “You look at all the candidates and there’s not many about.
"For years you have always had two or three players who could actually be England captain but at the moment I don’t see a stand-out one.
“Wayne Rooney is our best player as far as I’m concerned at this moment in time, and maybe Wayne is the one who will get the armband.”
Robson, who made 345 appearances for United, has called on new manager Louis van Gaal to act quickly in sourcing experienced replacements for Nemanja Vidic and Patrice Evra, who have joined Inter Milan and Juventus respectively.
Van Gaal has already signed England left-back Luke Shaw from Southampton but Robson is looking for cover in the centre of United's defence.
“We have still got Chris Smalling and Phil Jones at the club but I would like to see maybe another experienced centre-half come in," he said.
And Robson is also convinced the lack of European football next season will work in United's favour as they bid to reclaim the Premier League title.
“Not being in Europe where the lads have been used to playing at the weekend, midweek and weekend again, means they’re going to get a few weeks where they won’t have a game.
“The preparation time for the manager is going to be really good to get the players to understand exactly what he wants and whatever role he wants them to play in. So I do think we can bounce back straight away and challenge for the title.”