Novak Djokovic celebrates a point against Germany's Philipp Kohlschreiber during their 2014 US Open fourth round match in New York, on September 1, 2014
Eighth-seeded Murray -- born a week before world number one Djokovic -- triumphed over his Serbian rival at Flushing Meadows two years ago to lift his first major title.
The pair have a long career rivalry which the Serbian leads 12-8, while the pair stand at 2-2 in Grand Slam finals.
"We've had a lot of long ones," Murray, 27, said ahead the looming night-time contest in the Arthur Ashe Stadium.
"We played a long one here a few years ago -- I have great memories from that match," added the Scot.
Murray advanced to the last eight with a hard-fought three-set victory over ninth-seeded Jo-Wilfried Tsonga, avenging a loss to the Frenchman in the Toronto Masters last month.
Top seed Djokovic, the 2011 US Open champion, defeated Germany's Philipp Kohlschreiber 6-1, 7-5, 6-4 on another oppressively muggy New York day on Monday.
Djokovic's victory saw him reach his 22nd straight Grand Slam quarter-final, a run that stretches back to Kohlschreiber's victory over him in the third round of the 2009 French Open.
"I'm very glad obviously that I had so many consecutive quarter-finals of Grand Slams. It says that I do value these tournaments the most and try to always perform my best tennis in them," Djokovic said.
In 2012 Murray and Djokovic equalled the record for longest US Open final at four hours and 54 minutes.
Djokovic beat his long-time rival in the final of last year's Australian Open but Murray turned the tables at Wimbledon a few months later.