The 34-year-old midfielder has also reiterated his wish not to succeed Brian Kerr as the manager of the Republic of Ireland if he is sacked next week.
Kerr is set to lose his job if Ireland, who have qualification games away to Cyprus and at home to Switzerland, fail to make the play-offs for next year's World Cup.
Keane is undoubtedly interested in the post but, crucially, only in a couple of years' time when he has finished playing and when he has gathered the coaching experience he wants.
He is also mindful of the fact that it was Kerr who wooed him back into the international squad after his walk-out before the last World Cup and does not want to be disloyal.
Keane, whose current deal at United runs out in July, will investigate opportunities abroad, possibly in the Netherlands or France, rather than at Celtic or in England.
Keane wants to be exposed to the techniques and training of a foreign club. Nothing has been decided yet although several options, including player-coach posts, have been raised. There is still a strong chance he will stay at Old Trafford.
It is understood that Keane believes moving to Glasgow might increase, rather than lower, the attention on him at a time when he is planning a new phase of his career.
If anything Celtic is more of a "goldfish bowl" than United and, additionally, Keane believes his presence may simply add to the pressure on the manager Gordon Strachan who, in any case, may not want him.
Keane's thinking shows how serious he is about becoming a manager.
Senior officials at the Football Association of Ireland have already discussed approaching Keane if Kerr is sacked. But any offer will be firmly rebuffed.
The FAI is also likely to try and approach former Celtic manager Martin O'Neill - who stepped down to look after his wife, who has lymphoma cancer - or Aston Villa manager, and former Irish international, David O'Leary.
The organisation, now headed by chief executive John Delaney, who is not regarded as a fan of Kerr's, will certainly go for a higher-profile manager should they opt for a change.
If they did persuade O'Neill, who is from Northern Ireland, it would represent an astonishingly bold appointment. Kerr, the former FAI technical director, is tipped to accept a post with Uefa should his contract not be renewed.
Having succeeded Mick McCarthy after the disastrous start to the campaign to qualify for Euro 2004, Kerr's reign started promisingly. However Ireland fell short of reaching Portugal while Kerr has become an increasingly beleaguered figure. He has also failed to see eye-to-eye with Delaney who did not support his appointment in the first place.
Keane, who is out for two months with a broken metatarsal bone in his left foot, will miss Ireland's next two games, and captain Kenny Cunningham was stark yesterday in stating exactly what is required.
"We need two wins from the two games, anything less we are going to miss out," he said. "We have to go to Cyprus and be positive we have to go and win. Things are now black and white for us. There is no in-between, no grey areas."
Ireland's campaign has faltered, amid accusations of unambitious football, with two draws against Israel and a home defeat to France but Cunningham stressed that there was no point now having any regrets.
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