The 62-year-old veteran will only accept the chance of fulfilling his ambition to manage in England if he’s got a sidekick to work alongside that is familiar with the terrain.
While Ryan Giggs, installed as manager yesterday in place of the sacked David Moyes on a temporary basis, would appear to meet the criteria, Van Gaal is understood to favour a fresh voice and someone with at least some level of managerial experience behind him.
The former Barcelona, Bayern Munich and Ajax coach has been a long-time admirer of Keane, both during his playing career and brief foray into management.
In 2001, Van Gaal stood forlornly on the Lansdowne Road sideline as the midfielder’s man-of-the-match performance proved integral to a 1-0 victory Ireland secured which ended the World Cup qualifying ambitions of his Dutch side.
The choice by the notoriously aloof Dutchman of Keane, who skippered Manchester United during their most decorated ever period during the late nineties, would meet with approval of a fanbase desperately craving the restoration of principles which underpin the club’s successful tradition.
The obvious barriers to Keane’s United return are not insurmountable.
His bitter fallout with former manager and current director Alex Ferguson will not be a showstopper as Van Gaal is to have carte blanche on his backroom staff.
Nor too will be the Corkman’s employment as Martin O’Neill’s assistant of the Ireland team.
O’Neill has openly acknowledged the existing risk of losing his companion to club duties, albeit maybe not within only seven months of the dream duo taking charge of the Republic’s football future.
The €1 million compensation package due to the FAI for the remainder of Keane’s two-year contract is a pittance of an outlay to the Glazer family in the context of potential returns accruable from getting this appointment right.
The FAI last night refused to comment on Keane’s possible departure.
Keane, now 42, is pragmatic enough to realise this may be his best chance of eventually reaching the Old Trafford hot seat.
Having ended his 12-and-a-half-year association with the club in 2005 under a cloud, it is ironic that the club’s lowest ebb in 28 years might be the making of him.
The Irishman certainly struck a chord with the frustrations of United fans when speaking on television last night about the sacking of Moyes.
In typical Keane fashion, he cited the on-field substandard displays of players — rather than the management on the sidelines — for the club’s woes. "I think some of the players at Manchester United should be ashamed of themselves," blasted Keane on ITV.
"I think they have really let him (Moyes) down. I think it is a shame because I think he should have been given more time.
"He certainly had a hard start when he took the job.
"I think the chief executive didn’t get the deals done that he wanted. There was a lot of negativity.
"He had a slow start and no momentum."
Keane passed up the opportunity to continue his public fed with Ferguson, absolving his former mentor of blame for choosing Moyes as his successor.
He said: "I wouldn’t necessarily say it was his (Ferguson’s) pick, obviously he put his (Moyes) name forward but the club had to make the decision. You can’t be critical of Alex Ferguson.
"For David Moyes to be seventh in the league is disappointing and he takes responsibility for that. But you still need good people around you to help you in any way they can.
"I don’t think he’s had that support, particularly from the players. I think he should have got a bit more time — definitely."
The fact Van Gaal will be in Brazil with Holland for the World Cup this summer will not be an obstacle to the Dutchman taking over.
His hopes of becoming United’s next boss were boosted by Borussia Dortmund coach Jurgen Klopp and Bayern Munich boss Pep Guardiola swiftly ruling themselves out of the running.
"Man United is a great club and I feel very familiar with their wonderful fans. But my commitment to Borussia Dortmund and the people is not breakable," Klopp said.
Pep Guardiola was considered when Ferguson retired last summer, but the Spaniard went to Bayern Munich, where he intends to remain.
"I want to stay at Bayern for two more years," Guardiola said.
In the short-term Giggs is expected to be assisted by Nicky Butt, who is currently in charge of the U19s and also coaches the reserves.
Phil Neville and Chris Woods remain in their posts as first-team coaches, but Steve Round and Jimmy Lumsden — both brought in by Moyes last summer — have been fired.
A throng of camera crews and photographers turned up at the AON Training Complex, but they had missed Moyes, who slipped in during the early hours of yesterday morning.
Moyes was sacked shortly after 8am, but the 50-year-old remained at the training ground for a few hours so he could thank and say goodbye to his players.
He then left via the back exit away from the cameras.
The list of unwanted records broken by Moyes is as embarrassing as it is long.
United are guaranteed to end the season with their worst points total in Premier League history, they have failed to qualify for the Champions League for the first time in almost two decades while Moyes’ home record is the worst of any United boss since 1978 when Dave Sexton was in charge.
As a result Moyes will go down in history as the third shortest serving United boss behind Walter Crickmer and Lal Hilditch.