Gasquet, who has not played since Miami, said his back injury improved after treatment but that he is lacking practice after a six-week layoff.
"I just began to serve again," he told Eurosport. "It was not easy. I just began to play points again as well."
The 27-year-old is expected to say whether he will play by Saturday, a day before the tournament begins.
Monfils has withdrawn from Nice with an ongoing ankle injury. "I moved around but not enough to play singles," he said.