- Ryder Cup
McIlroy & Woods disagree over next Ryder Cup captain
Instead, the world No. 1 has urged Clarke to delay his bid to become captain of Europe until their return to American soil in 2016.
McIlroy, who was dumped out of the World Golf Final by Tiger Woods in the last of his round-robin matches in Turkey on Thursday morning, has tipped Paul McGinley to captain Europe in 2014.
"I always thought Clarkey would be a better captain in the US," McIlroy told Sky Sports News. "If it was up to me I would like to see McGinley as Ryder Cup captain in 2014 and Clarkey as captain in 2016 - I think that would work better."
In contrast, Woods believes there is nothing stopping selectors from turning to the 44-year-old to lead the side at Gleneagles.
"I think he would make a great captain," Woods said. "Darren's one of my best friends out here and he's just a great guy.
"I think he would make a great leader and I don't know what the process is for you guys to select your captain, but if he is he would be a great one."
"This all seems a bit premature, doesn't it?" asked Rose. "I know he (Clarke) sent out a tweet last night saying, 'Listen it [the announcement of the next captain] is in January, just calm down everybody'. But he'd make a great captain, as and when it's his time, for sure."
Westwood reiterated Rose's belief that such talk was premature, adding that Clarke himself wouldn't appreciate people "already giving it to him".
"I'm sure he'd take it if he was offered it, and I think he'd make a good captain. He's got all the credentials - recently won a major championship, he's been great in the Ryder Cup, played five of them, won countless tournaments.
"He's a good speaker, good motivator, so I've no reason not to think he'd be a good captain if he got it."