Tuesday's European Tour tournament committee meeting in Abu Dhabi will discuss who takes over from Jose Maria Olazabal and Paul McGinley, an assistant in the last two matches, is favourite now that Darren Clarke has stated his desire to regain a place in the team.
At a press conference in Abu Dhabi to announce his new sponsorship deal with Nike, McIlroy said: "I feel like everyone deserving should get their chance. I played under Paul at the Seve Trophy in 2009 and thought he did an unbelievable job. Of all the captains I've played under he would be the best."
He added: "It's the small details. He does not leave any stone unturned, he gives great confidence in the team room and I think he would make a really good captain. I am really behind Paul and I think he should get the job and I hope that he does.
"I don't think Monty has anything to gain if we go to Gleneagles and lose. He is already a winning Ryder Cup captain."
Gallacher captained Europe on three occasions, but told Sky Sports News: "There are many more potential candidates for the job now and I would go along completely with Rory McIlroy. I think it's a one-term appointment now to give other people a chance. In my opinion Colin should step down to allow Paul a clear run at the job because he is the person with all the credentials for the job."
Ian Poulter and Luke Donald, also members of the winning team with McIlroy at Medinah, have also stated their preference for McGinley. Donald queried on Twitter whether Clarke had dropped out of contention and added: "If so probably the correct decision as he still has a chance to make team and would make a great captain on US soil in 2016.
"I hope Paul McGinley gets his chance, he's been an amazing Vice Captain and deserves an opportunity #2014RyderCup."
Poulter answered Donald's question as he wrote: "Darren has taken his name out of the running for Ryder cup captaincy. It would be fantastic to have Paul Mcginley as the 2014 captain."