The 29-year-old centre forward joined Charlton initially on loan from Preston North End in the winter of 2021 and later made the move permanent in the summer.
Last season, Stockley made 38 appearances in all competitions and managed to net 20 goals.
But this season, goals have dried up for the forward, scoring only three times in 29 appearances.
Under new manager Dean Holden, Stockley has lost his captaincy and spot in the starting line-up.
And Charlton are willing to part ways with the Englishman in the ongoing transfer window, with Fleetwood Town and Gillingham interested in his services.
However, it has been claimed that Stockley intends to compete for a spot in Holden’s team and has no plans to leave Charlton in January.
Fleetwood manager Scott Brown is an admirer of Stockley and wants to add the striker, but the 29-year-old’s high wages could be an issue for the Fisherman.
Gillingham meanwhile sit second bottom of the League Two table and are keen to add goals, having netted just eleven times all season.
