The Frenchman has been heavily linked with a switch away from QPR this summer and saw an £8m move to Liverpool collapse after failing a medical last month.
Remy started his club's 1-0 home defeat to Hull City on Saturday, and Simpson claims that the 27-year-old is content with life in West London.
"He looks like he's happy here and wants to stay. It will give us a boost if he does," Simpson told Sky Sports.
"I think Loic showed the fans he wants to play and he was unlucky not to score today. It was his first game for us and he hasn't played much pre-season.
"He can only get better and he will do well."
James Chester scored the game's only goal to spoil QPR's Premier League return following their promotion from the Championship.