The British No1, who received a bye in the first round in Toronto, set up a clash with the Frenchman after overcoming Xavier Malisse in straight sets 7-5 6-2 on Wednesday night.
And the 23-year-old is expecting a tough challenge against world No18 Monfils as the Scot looks to continue the defence of his title.
“It will be a fun match,” Murray told Sky Sports after beating Malisse in the second round in Toronto.
“He’s probably the best athlete that’s ever played the game. He’s so fast, he can jump incredibly high and reaches most balls so it’s going to be difficult.
“I’ve played well against him in the past. You have to change the pace a lot because when he’s just moving side to side he doesn’t miss a whole lot.”
Murray added that he would continue to work without a coach in the build-up to the US Open and stressed he is in no rush to find a replacement for Miles Maclagan, who he parted company with last month.
“When you’re on your own, you have to play the way you like and come up with your own tactics, work things out on court a little better, and it’s actually a nice feeling,” he told BBC Sport.
“I guess I’ll see how the next couple of weeks go and how I feel on the court.
“But I don’t want to rush into making a decision just for the US Open and you end up with someone that isn’t going to work and you aren’t getting on with.
“I’ve got a break after the US Open when I’ll probably sit down and have a long think about what I want to do and who I want to work with.
“That’s probably the best time to do it because I don’t want to make a bad decision before a Grand Slam.”
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