The 46-year-old, who is not involved at Gleneagles this weekend, has featured at the tournament seven times - five as a player and two as a vice captain.
World number one Rory McIlroy recently backed reports that Clarke will be given the skipper's responsibility at Hazeltine and when asked for his opinion, the veteran Northern Irishman revealed that he would view the role as the "ultimate honour".
"I would love to be [the next Ryder Cup captain], but that's not up to me, and if [the European Tour committee] were to offer me the job I would certainly not be picky as to when it would be," he told Sky Sports News.
"It would be too big an honour to differentiate between doing it in America or doing it in Europe. But, certainly, I've always been fortunate throughout my career that I seem to have been quite popular with the American fans, who have always been very, very good and very, very kind to me.
"Wherever it is, I just hope at some stage that they do ask me to have the ultimate honour and be Ryder Cup captain. Playing records and everything come into it, but there is no interview and it's for whomever the committee think is the best man for the job."
This year's instalment of the Ryder Cup will get underway on Friday.