Darren Clarke and Paul McGinley, two of Jose Maria Olazabal's assistants as Europe amazingly retained the Ryder Cup from 10-4 down, are seen as the two leading candidates to take over from the Spaniard for the 2014 match at Gleneagles.
The European Tour's tournament committee chaired by Dane Thomas Bjorn, another of the vice-captains in Chicago, will be expected to make a decision in January.
Rory McIlroy believes that whoever is chosen "will be a great captain", but added: "I've always said I think Clarkey would be a great captain here in America. I think the crowds really love him, so maybe save Darren for 2016."
McIlroy played under McGinley's captaincy at the 2009 Seve Trophy in Paris and commented: "He was fantastic there and has also been a fantastic vice-captain."
Olazabal also called on compatriot Miguel Angel Jimenez at Medinah and McIlroy stated: "They are all different and all have their own opinions, but collectively they are very knowledgeable."
The Americans are likely to name their successor to Davis Love in December and there are bound to be calls for successful Presidents Cup captain Fred Couples to step up from being an assistant this time.
Couples, however, has already agreed to stay on for a third match against the International side. It takes place at Muirfield Village in Ohio in October next year.
That could open the door for someone like 45-year-old David Toms, a member of three Ryder Cup teams.