Bale moved to the Spanish giants from Tottenham at the start of the 2013-14 season for what was widely reported to be a world-record fee.
The 25-year-old has made an impressive start to his Real career, having already won the UEFA Champions League, Copa del Rey, UEFA Super Cup and Club World Cup.
United dominated the headlines in the last transfer window by bringing in Angel di Maria from the Santiago Bernabeu for a British record sum, and there has been rumours that Van Gaal has his eye on making Bale another high-profile signing.
And when questioned about that link in a press conference on Tuesday, the Dutchman did not unequivocally rule it out.
"I cannot discus that with you," he said.
"I discuss that with my CEO [Ed Woodward] and not with anyone of the media."
