Dutch boss van Gaal was greeted by waiting Red Devils fans following United’s FA Cup final win over Crystal Palace at Wembley on Saturday.
When asked by a Sky Sports reporter if he had time to talk, van Gaal replied: “It’s over.”
Whether that meant he had been sacked by United was not immediately clear.
But the 64-year-old former Netherlands manager’s brief remark will fuel speculation he is on his way out of Old Trafford.
No sooner had United lifted the FA Cup then reports in the British media emerged that former Chelsea boss Mourinho would be replacing one-time mentor van Gaal.
For all that they ended this season with a trophy, United didn’t make a sustained challenge for the Premier League title and failed to qualify for the Champions League.
United fans were also unhappy with the brand of football their team played under van Gaal, which many felt ran counter to the club’s traditional attacking style.
Mourinho saw his second spell as Chelsea manager end with the sack in December after last season’s champions made a miserable start to the defence of their Premier League title.
The Portuguese manager may have won trophies in several European leagues but has never stayed at one club longer than three years and three months he racked up in his first spell with Chelsea.
But former United defender Phil Neville said even if Mourinho was only at Old Trafford for a brief time, he would bring trophies to the club.
“I can’t see him staying too long at Man United, maybe two or three years, that seems to be his shelf life at a football club,” Neville told BBC Radio on Sunday.
“When Jose finishes at a club it tends to be a pattern where he falls out with a few players, he gets disgruntled and the team dips.
“It happened at Chelsea, it certainly happened at Real Madrid where there were rumours he fell out with a few players.
“It’s a pattern with Jose, he comes into a club, he gets success but he doesn’t stay for too long.”
United have now failed to finish higher than fourth in the Premier League in any of the three seasons since legendary manager Alex Ferguson retired.
For a club of United’s stature that represents an embarrassing record but Neville believes Mourinho, who won three Premier League titles with Chelsea, can transform their fortunes.
“He’s a proven winner, a proven champion,” Neville said.
“United fans want a team that will challenge for the league title, not a team that finishes seventh or fifth, and Jose is probably the man for the job.
“Knowing Jose as I do, I think he will have done his homework and he’s meticulous in his planning.
“He knows who he wants and at the start he will demand United sign those players for United to become championship challengers again.”