The Dutchman, under pressure after seven games without a victory, was asked at his post-match news conference whether he feared he would be sacked.
Van Gaal, 64, said that was something he would discuss with executive vice-chairman Ed Woodward and not the media.
"It is not always the club that has to fire or sack me," he said.
"Sometimes I do that by myself, but I am the one who wants to speak first with the board of Manchester United and my members of staff and my players, not with you."
Van Gaal, who succeeded David Moyes in the summer of 2014, said the club had backed him "all the time" but added: "We have lost so there is a new situation.
"I feel the support of my players and my board. The fans will be disappointed but that is logical after four defeats."
Van Gaal does not think it is important that Woodward has not publicly supported him.
"For me it's much more important that people are saying that to me," he said. "I am not so interested in public sayings."
With United facing Chelsea at Old Trafford on Monday van Gaal might have some serious decisions to make if they lose. Wayne Rooney looks sure to be restored to the strating line-up but with many United fans clamouring for former Chelsea bos Jose Mourhino to take over in the new year it would be ironic if his former side are the ones that ensure he gets the Old Trafford gig.
United have not beaten Chelsea since 2012 and facing them on the back of a poor run of form will not help. It will be an intriguing game with much more tha three points at stake.