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.
Rumours of a possible stay in West London increased when Remy started Saturday's 1-0 defeat to Hull City, and Barton says that he is "keen to stay" - providing a Champions League club do not come calling.
"For me, he is keen to stay," the 31-year-old is quoted as saying by The Mirror.
"If a Champions League club comes in for him, could anybody blame the lad for going? I don't think I would and I don't think any of the fans would.
"But that is the big if: If a Champions League club came in for him. There aren't many of them."
The 27-year-old's contract expires in 2017.