England are without a permanent coach or captain after John Terry was stripped of the armband by the Football Association pending a racial abuse trial and manager Fabio Capello quit in protest.
"For everyone asking, I would love to be England captain. But that's up to new manager to decide. Gerrard is perfect choice for me," Rooney wrote on his Twitter feed.
Rooney, who can not play in the first two Euro 2012 group games against France and Sweden because of suspension, is seen by pundits as an unlikely pick for captain with Gerrard the bookmakers' favourite for the role whoever takes over as coach.
Under-21 boss Stuart Pearce is in temporary charge for this month's friendly against Netherlands with Tottenham Hotspur manager Harry Redknapp tipped by Rooney and the media to be approached about becoming the full-time coach before or after Euro 2012.
FA Chairman David Bernstein is determined not to rush an appointment and said age was no barrier to 64-year-old Redknapp.
"I can understand the hype around Harry. The guy has done amazingly," he told British newspapers on Sunday.
"He is a fine manager and he is English. This job will be so attractive to many people, we will get interest from serious parties in spite of this hype."
Rooney's preference for midfielder Gerrard as captain comes after the forward scored twice as hosts United beat Liverpool 2-1 on Saturday in a game marred by Luis Suarez refusing to shake Patrice Evra's hand.
Liverpool striker Suarez was banned for eight games for racially abusing Evra in October and his fresh antics were followed by scuffles in the tunnel at half-time between the teams, who are fierce rivals and whose animosity has previously spilled over into the England setup.
Britain's Sunday Telegraph said Prime Minister David Cameron is to stage a summit on racism in football following the Suarez and Terry cases.
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