The 32-year-old has been with Charlton since joining from Leicester in 2011.
He has impressed during his time in South London, hitting double figures in each season has been with them so far.
Now Bournemouth, who are anxious to bolster their attacking options, have lodged a bid for the target man.
Kermorgant's current deal expires in the summer, although there is an option for Charlton to extend it.
Celtic boss Neil Lennon has also shown an interest in the Frenchman and watched him score twice against Oxford in the FA Cup earlier this month.