Colin Montgomerie has confirmed that he will be stepping down as Captain after what he called "the greatest and proudest moment of my career" - the nail-biting one-point victory over the Americans at The Celtic Manor Resort on Monday.
"This is a one hit - I will not be doing this again," he said. "I think it's only right that it should be shared around."
Later, asked about who he would like to see take over for Medinah, Chicago in 2012, Montgomerie replied: "I do hope José Maria will be well enough to be the next Captain.
"He did brilliantly as one of my assistants here and it was also only right that we had a picture of him and Seve (Ballesteros) in our team room and then at the closing ceremony.
"It was between him and me for the captaincy this time and in two years' time he'll be 46, just a year younger than I am now."
Olazábal and Ballesteros formed the greatest partnership in Ryder Cup history, losing only two of 15 games together, and both played their part in last week's victory.
Ballesteros, battling brain cancer, was linked up to the team from his home in Spain for a passionate and inspirational call and was among the first to send a message of congratulations to the Team after their victory.
Olazábal, Nick Faldo's Vice-Captain two years ago, joined the backroom staff only on Saturday.
He has played only once this year because of his continuing fight with rheumatism, but is due to return to action at the CASTELLO MASTERS Costa Azahar later this month.
"I would love to do it," he said. "It all depends on my physical situation, but it's much better than it was a few months ago."
Paul McGinley, one of Colin Montgomerie’s Vice-Captains was also asked if he would like to take over the reins but he too spoke up for Olazábal.
"It would be great if the honour comes my way, but I hope Olly will be next," he said. "Fingers crossed for him."
Montgomerie's Ryder Cup career will go down as one of the best ever.
Never beaten in singles and a member of five winning teams as a player, he now has a victory as Captain as well.
"I didn't hit a shot so it wasn't much of an achievement, but what a match," he said.
"I had 12 special guys, I asked them to play with their hearts and with passion and by God they did."
Montgomerie admitted the result was clinched in Sunday's session.
Graeme McDowell's 3&1 win over Hunter Mahan, on an historic extra day on Monday, ultimately proved decisive but it was the contest's third session - in which Europe took 5 ½ points from six across two foursomes and four fourballs - which set up an eventual 14 ½ -13 ½ win at Celtic Manor.
Montgomerie said: "We won this Ryder Cup on Sunday night by having that fantastic session of 5 ½ to a ½ . That's where we won The Ryder Cup, it wasn't actually yesterday.
"But we needed to maintain that momentum, we knew the Americans would come out strong and they did. Lee Westwood was put out first, he's our strongest player, and he lost (2&1 to Steve Stricker) and you thought 'hang on a minute, this might not go the way we were hoping for'.
"There were some great results. Miguel Angel Jiménez, at 46, to come through that way (4&3 against Bubba Watson), Luke Donald's victory (over Jim Furyk) down the last hole - and of course G-Mac (McDowell).
"To hold him as 12th man was a good decision by us all. He is the Celtic Manor Wales Open champion on this course, he's the current US Open champion - he was put there for a reason because he can handle himself in that situation.
"That birdie on 16 will live in my memory, and live in all our memories, for a long time."
