Both men hope to be in the playing lineup when Europe defends the title at Oakland Hills Country Club, Michigan, in 2004. Either Bernhard Langer or Ian Woosnam is expected to take over for Sam Torrance, who was captain of the team which beat the Americans at The Belfry in September.
The 2006 Ryder Cup will take place at the K Club in County Kildare, Ireland. Both Montgomerie and Faldo want the captain's job then.
Montgomerie was Europe's biggest star at The Belfry, going unbeaten in five matches as the home team regained the trophy 15 1/2 to 12 1/2. The 39-year-old Scot aims to play at Oakland Hills and then lead the team as non-playing captain two years later.
'It depends how I feel, how the (European Tour) committee sees it and how it all pans out,'' Montgomerie said Wednesday. 'But I would like that and I have mentioned that to the powers that be so they have that on the record.''
'I will have played under four or five captains by then and hope I will have learned from them all. Sam is the best and if I did half as good a job as him I would be very happy.''
Faldo, who has played in 11 Ryder Cups, didn't make the 2002 team. But he believes he still has the game to get back onto the team for 2004. After that, he covets the captaincy.
'It's gone from not being spoiled for choice to people queuing up,'' he said.