David De Gea was dropped for United's 1-0 win over Tottenham on the opening day of the Premier League season with Van Gaal suggesting that the goalkeeper was not in the right frame of mind to play amid Real Madrid’s interest.
Reports have claimed that Cillessen has been identified as Van Gaal's first-choice replacement for De Gea - but the Netherlands international maintains that United have not been in contact.
"I've read that this weekend I have spoken with Van Gaal," Cillessen told Het Parool.
"But the last time I did was during the Sports Gala late last year. My management has heard nothing."
Ajax coach Frank de Boer also admitted last week that United will need to pay a “huge price” in order to sign Cillessen.
"To make it clear, Jasper is getting more expensive by the week, although there are certain figures that we can't turn down,” said the 45-year-old.
