Van Gaal reacted jubilantly to Ashley Young’s late goal in United’s 1-0 victory over Newcastle United at St James’ Park on Wednesday.
In marked contrast, Giggs greeted the dramatic winner in subdued fashion and failed to react when van Gaal playfully jabbed the Welshman in the face as he celebrated.
But van Gaal dismissed press reports of a breakdown in their relationship, saying: “I don’t want rumours. I am irritated by this question because everybody can see we have a good relationship. Not only with Ryan, but that goes for all the staff and players.”
Giggs was appointed van Gaal’s assistant last year after taking charge of the first team for four matches in a caretaker capacity last season following the sacking of David Moyes.
The 41-year-old former midfielder has been earmarked as a future manager at Old Trafford and potentially a successor to van Gaal in 2017.
When asked about his rapport with Giggs at his weekly press conference, van Gaal initially joked that they had a “very bad relationship”, before revealing his annoyance with questions on the subject.
“I think it’s a way of suggesting things, so I’m very irritated,” he said. “I’ll take this up with the media. I’m not pleased.”
Van Gaal also said he believed what defender Jonny Evans has told him about being innocent of spitting at Newcastle’s Papiss Cisse.
Evans issued a statement on Thursday in which he denied that he spat at the Senegal striker, who has himself apologised for spitting at the United man.
The Football Association have charged both players over the incident, which means they could face a six-match suspension.
“I have spoken with Jonny Evans,” van Gaal said. “He wasn’t aware that he was spitting and when he was spitting on the ground, maybe that is a natural thing from a human being.
“It was not his intention and that I said already. I cannot imagine that Jonny Evans could do that and he has said that also. I believe him, so for me the matter has been done.”
United face Arsenal in the FA Cup quarter-finals at Old Trafford on Monday and Van Gaal said the game could have repercussions for the pair’s tussle for Champions League qualification in the Premier League.
“I think if we beat them it is a big blow for them, but if they beat us it is a big blow for us,” said the Dutchman.
“It is a very important game, not only for the FA Cup, but also for the rat race. We have the support of our fans, but Arsenal shall also bring a lot of fans. I hope we can give a fantastic match for them.
“Usually against the likes of Arsenal and Chelsea, you have to be at your best.”
United have no fresh injury concerns ahead of the match and the club’s medical staff will assess left-back Luke Shaw after he missed the game against Newcastle with a tight hamstring.