Ryan Giggs was installed as interim manager after David Moyes departed the club last week, leading to widespread rumours about who will succeed the Scot on a long-term basis.
Current Netherlands coach Louis van Gaal has been touted as the favourite, with suggestions that Keane could rejoin United as the Dutchman's number two.
However, Keane, who currently works alongside Republic of Ireland coach Martin O'Neill, distanced himself from the post in an interview with Today FM on Monday.
"No, I don't think that way," he said.
"In my quiet moments, I obviously want to go back into being a manager myself.
"I was at a match on Friday night, I was at a match on Saturday and I am up in the stand thinking, 'I would love to have a team.'
"And then I'll get back in my car and I spoke to Martin, and then I am thinking obviously I am delighted to be working with Martin and (goalkeeping coach) Seamus (McDonagh) and the other staff, so you have to be careful what you wish for.
"I am just really appreciating the opportunity I have at the moment. What happens further down the road..."
Keane fell out recently with former manager Alex Ferguson following comments made in the latter's autobiography and the United legend is unsure whether he can foresee a time when the two are back on speaking terms.
"No, I am not sure. Probably not," he said. "But look, I have said that about other people.
"Football is a funny old game and you get clashes of personality sometimes, but it's something that's not on my mind at the moment, to be honest with you, whether it be good or bad."
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