Olivier Giroud has played in just five games for Chelsea this season, scoring a solitary goal.
He has been vocal about his frustration at a lack of game-time before, as has the French national team manager Didier Deschamps.
“You know, Olivier suffers his situation. Before January, nothing will move,” Deschamps told the press.
“After, it will be up to him to see. I hope he will have more playing time.
“But we cannot take away his goals, his good performances. He scores, he makes others play well."
Crystal Palace boss Roy Hodgson shares Deschamps's admiration for Giroud and wants to recruit him in January, according to the Sun.
Hodgson wants a Premier League proven goalscorer to help bolster his attack this season for what could be a surprise challenge for European football.
Giroud's current deal runs out at the end of the season, so it's believed the 33-year-old would be available on the cheap (around £3m).
Fellow Blue, Michy Batshuayi, enjoyed a successful loan spell at Selhurst Park last season, but Palace have been rebuffed in an attempt to bring the Belgian in permanently.
Lampard is reluctant to let go of important players while Chelsea are under a transfer embargo, but Giroud's place in the pecking order makes an exit more palatable.
Palace could face competition from Inter Milan for Giroud, but the player is thought to prefer staying in London, where he's played his football since 2012.
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