Nice president Gauthier Ganaye says his club could move for Olivier Giroud this summer.
Giroud has been linked with a number of clubs in his native France but his wage demands could make a move difficult.
However, Ganaye has suggested that Nice will try to thrash out a deal to sign him.
“He is at the end of his contract, he still performs well at his age,” Ganaye told Telefoot, as reported by Goal.com.
“Come on, let’s tell you it’s possible. His salary? Yeah, it’s really expensive.”
Chelsea have an option to extend Giroud’s contract by a year but the striker recently admitted at a press conference that he is frustrated at his lack of first-team football at Stamford Bridge.
“Trust me I am very frustrated when I am not on the pitch but I don’t want to show it,” he said.
“You need to keep that frustration and transform it into positive energy. Trust me I’m not happy to play the second role.
“Next year I will need to have a more important role to play.”
Giroud has scored nine Europa League goals this season but has started just 13 Premier League matches for Chelsea since being signed from Arsenal in January last year.
“The most important thing for me is to be happy on the pitch, to enjoy the game and to have more minutes,” he said.
“I’m a competitor. I really want to play more. It’s not that I’m 32 and won the World Cup so am ready to retire and will be happy with second place.”