The Dutchman oversaw a tense affair on Sunday in which the Old Trafford side took the lead right after the hour mark through Jesse Lingard, but saw themselves pegged back in injury-time by Diego Costa's equaliser.
United's draw sees them miss the chance to close the gap on fourth-placed neighbours Manchester City who lost 3-1 to Leicester City on Saturday, prompting speculation Van Gaal is to be replaced in the dugout by ex-Blues' boss Mourinho.
However, Van Gaal was having none of it and decided to turn the tables when facing the media after the match.
"Why does the club have to deny it when you are creating stories? You have not spoken to Ed Woodward, nor with the Glazers," the 64-year-old said.
"Maybe I can say that you are getting the sack tomorrow, what is your name? Maybe I can announce that. Write what you want. Maybe you also remember the first years of Sir Alex? Maybe you can look at the statistics."
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He continued: "That's why I am frustrated, because the gap is not going smaller. You can say it is misfortune but it is not the first time, Newcastle United was the same.
"For the third time in a row it was sparkling. I hope I will also get the support of the media this week!
"It's frustrating, not a big disappointment. We played well until the last quarter, and it's frustrating how they scored because Daley Blind was slipping.
"It is not easy to play here because the individual level of play is high in Chelsea. But it is better than last year, and last year we also played better than Chelsea I think but we lost 1-0.
"Now it's 1-1, so we improved!"
Nevertheless, Van Gaal took issue with the manner in which referee Michael Oliver brought proceedings to a close, and reserved praise for De Gea.
"When he whistled for full-time we were on the counter-attack, also in the first half," he said.
"So that was two times against Manchester United, so that is unfair. If you let them take the corner, you have to allow the counter-attack too."
"He [De Gea] was remarkable because they were nearly goals I think. They were fantastic saves."