Victorious 2010 captain Colin Montgomerie has been linked to the position a second time for next year's event in the eight-times European Tour order of merit winner's native Scotland, something McIlroy disagrees with.
"RC captaincy should be a one-time thing... Everybody deserving gets their chance and moves on... Would love to play under Paul McGinley in '14," twice major winner McIlroy said on Twitter on Sunday.
Darren Clarke, the 2011 British Open champion, is also in the frame though, with the Northern Irishman popular in the United States, he has been tipped for the 2016 job when the event moves back there.
Eight-times major winner Tom Watson, 63, was named as the 2014 U.S. captain for the biennial competition last month, having also captained in 1993 when he led the Americans to their last win on foreign soil.
Later this week, ahead of the Abu Dhabi Championship where McIlroy will open his season, Europe will vote on their captain for the 2014 edition at Gleneagles.
McGinley, who holed the winning putt on his Ryder Cup debut in 2002, has been quiet since his name was linked to the position.
"It's a big honor to be Ryder Cup captain but it's not something I want to commit myself to or say too much about," the three-times Cup winner said last year. "It's best if I just step away now and let things evolve. I'll just stand back and wait."
(Writing by Tom Pilcher in London, Editing by Clare Fallon)