Reports had claimed the Dutchman tendered his resignation after the 1-0 loss on Saturday but Goal understands they were wide of the mark.
Van Gaal labeled the stories suggesting he had to be persuaded to stay as "awful and horrible" on Thursday and has further reiterated his desire to continue at Old Trafford.
Asked about the claims he offered to walk away from the job, Van Gaal told reporters: "I have not mentioned that, ever. I am always fighting."
Van Gaal made clear he believes in honoring his commitments and does not think his job at United is complete.
"I have signed a three-year contract here. It's a process, not one game, and I want to continue until the end. When I'm not willing to do that, I don't think I would have started here one-and-a-half years ago," he said. "When I have signed for clubs, I have always spoken a long time with the CEO or with the owners, not only at United, but also at Bayern Munich and Barcelona, and I have the faith that they always support me.
"But that gives more pressure to you, because you must fulfil the expectations they have of you. Of course we can fulfil those expectations. We are now only halfway."
With United fifth in the Premier League and out of the Champions League and the League Cup, its FA Cup quest continues with a trip to Championship side Derby County in the fourth round on Friday.
And Van Gaal, claiming to have been sacked three times according to newspaper reports, added: "I cannot lose any more, because then I am condemned for the fourth time that I have been sacked.
"Then maybe you will have written the truth, because sometimes it happens."