Reports emerged on Tuesday (AEDT) suggesting the Dutchman spoke to United executive vice-chairman Ed Woodward about his future immediately after the English Premier League contest at the weekend.
Within that, there were some claims Van Gaal offered his resignation.
But that talk was dismissed by a club source as the 64 year-old returned to work.
After he and his players had both Sunday and Monday off, as was always scheduled, footage on Sky Sports News on Tuesday showed Van Gaal arriving to take training at the club's Aon Complex in Carrington.
Amid the intense speculation about his position and with him reportedly set for further discussions with Woodward this week, Van Gaal has United's next game to think about, Saturday's (AEDT) FA Cup fourth-round trip to Derby.
That match is looking increasingly important, with a poor result - or even just a lacklustre performance - against the Championship side only likely to increase the scrutiny on and anger from United fans towards Van Gaal, should he still be in his job by then.
Loud boos rang around Old Trafford after the final whistle of Sunday's (AEDT) game as Van Gaal endured what he later described as the worst reaction he has heard from United supporters during his time in charge.
He also said they were "right to boo" and said: ''I'm very disappointed that I cannot reach the expectations of the fans.
''They have, or they had, great expectations of me, and I cannot fulfil them.''
The Red Devils, frequently derided of late for playing in a dull, uninspiring way - had just one shot on target during the defeat.
They are now five points off the top four in fifth place, 10 points behind leaders Leicester and have won only three of their last 13 matches in all competitions, a sequence which has included seeing them exit the UEFA Champions League.