Van Gaal arrived at Carrington at around 8.45am (UK time). His entire coaching staff were also present as they learned their fate.
The 64-year-old was pictured waving goodbye as he left United's training ground base for what could be the last time on Monday afternoon.
Mourinho expects to have more talks ahead of signing a three-year deal with his long-term assistant Rui Faria and goalkeeping coach Silvino Louro expected to follow.
Ryan Giggs' future at United is up in the air despite Mourinho's wish to keep the Welshman at the club.
Van Gaal's trusted performance analyst Max Reckers, who caused friction within the Manchester United family, has also been shown the Old Trafford exit door.
Van Gaal was followed into United's training ground by employment lawyer Paul Gilroy QC, who has long worked with the League Managers Association.
Having initially been turned away by security, he was allowed into the complex around an hour after the Dutchman arrived.
Gilroy lists former United manager David Moyes among the clients he has advised, along with Sir Alex Ferguson, Roy Hodgson and Brendan Rodgers.
Chambers and Partners describe Gilroy as "a noted employment specialist" who is "renowned for getting a fantastic deal for managers".
Before the celebrations had even subsided at Wembley on Saturday, United's FA Cup win was being overshadowed by fresh reports that Van Gaal was to be replaced by the former Chelsea boss in the coming days.
United have steadfastly refused to comment on speculation regarding their managerial situation, while the Portuguese kept his counsel when asked about the job ahead of David Haye's fight on Saturday evening.
Van Gaal stood firm when asked about his position in the post-match press conference at Wembley, but fuelled speculation on Sunday by telling a reporter outside the team hotel that "it's over".
The brevity of the comment meant it was not immediately clear whether that meant the former Holland manager had been told his time at United was at an end.
Despite spending almost $555 million on players under Van Gaal, the club risked being left behind further if they didn't act.
Two years ago predecessor Moyes attended a morning meeting with Woodward at the club's training complex and a statement confirming the Scot's sacking followed shortly afterwards, just 10 months into a six-year deal to replace Ferguson.
Van Gaal still has a season remaining on his three-year contract, while Mourinho has been out of work since paying for Chelsea's abysmal title defence with his job in December.
The Portuguese has repeatedly spoken of his plans to return to work this summer, and reviving United's fortunes would surely be a mouth-watering proposition for the self-styled 'Special One'.
United, a club synonymous with a swashbuckling, attacking style, managed a paltry 49 league goals - their lowest return for 26 years - and missed out on Champions League qualification to neighbours Manchester City on goal difference.
A first FA Cup win since 2004 was a welcome boost, but captain Wayne Rooney admitted the campaign was far from good enough.
"He has been under pressure. I think we all have," Rooney said of Van Gaal. "That's part of playing for Manchester United and managing Manchester United - it is a massive club. You have to set standards and we fell below them this season."
