Victorious 2010 captain 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.
"I personally don't feel like Monty has anything to gain over this," the twice major winner said.
"If we go to Gleneagles and lose he's already a winning Ryder Cup captain. I'm fully behind Paul and I think Paul should get the job and hopefully he does."
World number three Luke Donald also voiced his support for McGinley when the Englishman wrote on Twitter on Monday: "I hope Paul McGinley gets his chance, he's been an amazing vice-captain and deserves an opportunity."
McIlroy played under three-times Ryder Cup winner McGinley for Britain and Ireland at the 2009 Seve Trophy against continental Europe and said his captaincy was awe-inspiring.
"He did an unbelievable job. (Of) any captain I've played under, I feel he was the best," said the 23-year-old, who opens his season at the Abu Dhabi Championship on Thursday.
"I think he'd make a really good captain. He doesn't leave any stone unturned. When he's been a vice-captain in the two Ryder Cups that I've played he's always brought a lot to the table and a lot of ideas."
McIlroy made his debut at the 2010 Ryder Cup under Montgomerie where McGinley served as a vice-captain, while the Irishman was also selected as a vice-captain under Jose Maria Olazabal in 2012.
McIlroy had already shown his support for McGinley on Twitter on Sunday, writing: "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."
Darren Clarke, the 2011 British Open champion, appeared to rule himself out of the frame last week when he said he wanted another shot at playing in the team.
The 44-year-old Northern Irishman is popular in the United States and 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.
Europe's 15-man committee, which includes McGinley, Montgomerie and Clarke, will vote for their captain on Tuesday.
Dane Thomas Bjorn, the world number 45, is the committee's chairman and could also enter the running, having served as a vice-captain in 2010 and 2012.
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 honour to be Ryder Cup captain but it's not something I want to commit myself to or say too much about," the 46-year-old said last year.
"It's best if I just step away now and let things evolve. I'll just stand back and wait."