The 61-year-old Dutchman is the front-runner to succeed the departed David Moyes at Old Trafford, though sources close to the club insist the Holland boss is only one of several names on a shortlist.
Those names include Real Madrid coach Carlo Ancelotti, but it is understood United chiefs will not change their mind and include Ryan Giggs on the shortlist despite a bandwagon building behind the club's temporary manager.
United, having had their fingers burned with Moyes, are determined to appoint a coach with a significant level of experience at the very top of European football and that rules out Giggs.
Giggs, however, could yet be number two to Van Gaal or another manager - especially now former United skipper Keane, who is currently working as assistant to Republic of Ireland manager Martin O'Neill, has ruled himself out.
Speaking to Today FM's Ray D'Arcy show in Cork, Keane said: "People keep asking me, ironically, about other jobs. I have got a job and I am very happy in my job."
Keane admitted he harbours hopes of a return to management one day, although he insisted that is not currently his main focus.
He said: "In my quiet moments, I obviously want to go back into being a manager myself."
Asked if his dream was for that to be at Old Trafford, he said: "No, I don't think that way.
"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, I think it was on Saturday night, 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..."
Van Gaal is keen to get a deal in place before Holland's World Cup preparations get underway on May 7, but United sources insist reports that one has already been agreed are wide of the mark. One report in Holland even claimed Van Gaal had met United owner Malcolm Glazer in Portugal - Glazer has not left the USA for years.
Keane, meanwhile, admitted his high-profile falling out with former United boss Sir Alex Ferguson is unlikely to be mended.
Asked if he could foresee a time when they two might be on speaking times once again, Keane replied: "No, I am not sure. Probably not. 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."