Reports of a feud between the pair were fuelled on Wednesday by their respective reactions to Ashley Young's late winner in a 1-0 Premier League victory at Newcastle United.
Both rose to their feet from the bench, but Van Gaal swiftly turned to Giggs, shouting and waving a clenched fist in his face.
Van Gaal's joy was not replicated by the Welshman, who remained stony-faced after seeing another stuttering performance from his side at St James' Park.
When pressed on the matter at a news conference on Thursday, Van Gaal said: "I cannot answer that," before sarcastically repeating: "We have a very bad relationship."
Re-assuming a more serious tone, Van Gaal continued: "I'm very irritated by this question.
"We have a very good relationship, everyone can see that we work very hard together, and that goes for all the staff and players.
"I'll take this up with the media, I'm not pleased."
