Mahut set up a second-round clash with the defending champion at Queen's by beating Guillermo Garcia-Lopez 6-4 6-2 on court one on Tuesday afternoon.
Murray, who received a bye through the first round, has beaten Mahut twice before. Mahut won just four games against the Scot at Indian Wells five years ago, but caused the 25-year-old problems the following year in Marseille where Murray edged through 7-5, 7-6 (7-5).
Mahut has a good record at the Wimbledon warm-up tournament, having reached the 2007 final after beating Rafael Nadal and he is optimistic about his chances of recording an upset on Wednesday.
"Of course I believe I can beat him (Murray). Otherwise I wouldn't be on the court," said Mahut, who took Roger Federer to four sets at the French Open 11 days ago after beating Andy Roddick.
"I beat Nadal once here. I was one point away from beating Roddick here when he was in the top five. I know I can do well.
"I know I can beat top players on this surface. I believe in myself, I believe in my game.
"He's the favourite but I just have to come on centre court, enjoy it and play my game.
"He is ranked fourth in the world but I played well the past few weeks, and I'm ready to fight."
Despite Mahut's bravado, Murray must be confident of progressing far in this tournament, with perhaps only Feliciano Lopez capable of stopping the Scot from reaching the final, where he is likely to face Jo-Wilfried Tsonga in a repeat of last year's title-deciding showdown.
Having recovered from a back injury which he suffered at the French Open last week, the pressure is on Murray to go beyond the semi-final placing he has achieved for the last three championships at Wimbledon.
But should he not successfully defend his crown here at Queen's, he will not be overly concerned.
He said: "Whether I win Queen's or not, I don't necessarily think it is going to change the outcome of Wimbledon.
"I have won here before and not Wimbledon so my goal is to obviously win Wimbledon.
"But it has always been good preparation for me to play here and get some matches under my belt on the grass.
"I feel pretty confident. I have been hitting the ball pretty well."
Murray has gone through a mixed patch of form since linking up with new coach Ivan Lendl over the winter.
The world number four reached the Australian Open semi-final, where he fought valiantly against Novak Djokovic, and then went on to reach finals in Dubai and Miami, but since then his best results have been quarter-finals in Monte Carlo and Barcelona.
Last week's French Open quarter-final exit to David Ferrer did little to convince Murray's doubters that he is in any kind of form to end Britain's 76-year wait for a men's singles champion, but the man himself is convinced his form will improve on the grass courts.
"I always like playing on the grass. I wish the grass court season was longer," he added
"I think all the players do. It is just completely different to anything else we play on the rest of the year.
"The two tournaments I play - Queen's and Wimbledon - are two of the best."
Murray has fond memories of playing at Queen's in particular.
"The first time I played here when I was 18. I won my first ATP match here," he said.
"That was nice and then I have managed to win the tournament a couple of times.
"It is not often you get to win a tournament or play a tournament in front of your friends and family so you get to celebrate with them as well, which is good."