Bernhard Langer, who guided Europe to a record 18-9 victory over the United States at Oakland Hills in September, announced Wednesday he will not return as captain in 2006.
Europe plans to select its captain on March 1 in Dubai, United Arab Emirates, and announce the choice the next day.
Woosnam and Faldo are the front-runners to lead Europe for the 2006 matches at the K Club at Dublin, Ireland. Sandy Lyle and Jose Maria Olazabal have also been mentioned as contenders.
Speaking at Thursday's launch of the British Masters at the Forest of Arden, Westwood said he favored Faldo, who was his partner when he made his Ryder Cup debut at Valderrama in 1997.
'I think they should all get it at some stage, but if I was asked to choose I would say Nick first,' Westwood said. 'I think they will give it to Woosie. I think he has more support on the committee.'
Westwood said the decision may come down to Faldo's record in 11 Ryder Cups against Woosnam's popularity.
'I would say Nick because he is the leading points scorer, has lots of experience, six majors, brought a lot of glory and would have the respect of anybody who plays,' Westwood said.
'He says he wants it and it is the right time, so he should get it. But I am sure there are still some anti-Faldo people. He has always been very single-minded and not endeared himself to people maybe as much as Woosie has.'
Teammate Darren Clarke said it was difficult to choose between the two and suggested one should be chosen for the 2006 match and the other for 2008.
'If there was a piece of paper I would tick both boxes,' he said. 'On past results you have to slightly favor Nick and in terms of relationship with the players Woosie would probably be slightly ahead.'
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