The 31-year-old recorded a routine 6-3 6-2 victory over American Rhyne Williams on a weather-affected day in London to set up a re-match with the world number two.
Murray, who missed the French Open with a back injury, has yet to play competitively on grass this season and Mahut is hoping to take advantage of that as he searches for another memorable upset.
"To play Andy here at Queen's is not a good draw, but last year I played amazing and I won the match," he said.
"So I hope this year it's going to be the same but everyone expect shim to win here, to win Wimbledon, so he has a lot of pressure on his shoulders.
"It will be much easier for me to play tomorrow. This is his first match here and first match for a month. I think if he's playing here it means he's feeling 100 per cent but still, it's the first round, especially on grass. I know he had some practice here, but still it's never easy to start a tournament, especially in the grass season."
Frenchman Mahut is also well remembered for setting the record for the longest match in tennis history when he lost to John Isner at Wimbledon in 2010.
The current world number 174 went on to reveal he enjoys grass more than any other surface and looks forward to competing at Queen's.
"I feel the atmosphere," he added.
"It feels like home here. I have known Chris Kermode for many years and he is the best tournament director on the tour. In 10 years I have played here every year. I really feel home and I love play on grass.
"To me, the grass season is always too short, but I don't know why. My best two victories have come here - I beat Rafa (Nadal) and I beat Andy last year."