The three-time Grand Slam winner and twice Olympic champion is eligible to compete in the singles at the Games with two places reserved for players who have previously won a Grand Slam or Olympics tournament.
However, Murray could miss out on the doubles in Paris with Britain set to send Joe Salisbury and Neal Skupski instead.
"I need to see what happens with the Olympics," he told reporters after his 6-3, 6-4 defeat to Marcos Giron at the Stuttgart Open on Tuesday.
"I'm not 100 per cent sure what the situation is there with the doubles yet and whether or not I will play if I just get in the singles. I don't know.
"My body didn't feel great playing on the clay in the last month or so. I had quite a few issues with my back, so I don't know if I would go just for singles.
"I need to wait a little bit and see on that," added Murray, who lost in the first round of the French Open doubles alongside Daniel Evans.
The tennis tournament at the Olympics will take place at Roland Garros from July 27th - August 4th.
