The 29-year-old is set to leave Selhurst Park after Palace recently confirmed he would not be offered a new deal.
The Wales international enjoyed a successful spell on loan with the Pilgrims at the end of the season as he helped them beat the drop.
Now Paul Sturrock is looking to entice Fletcher back on a permanent deal but is aware that he may face competition from a number of other clubs.
"The chief executive [Michael Dunford] and the agent are chatting to see what the story is," Sturrock told The Herald.
"Carl has shown an interest in coming to the football club, but there is still a lot of water to go under the bridge."
A stumbling block for the club could be the player's wages after Palace continued to pay a percentage of Fletcher's weekly income while he was on loan at Home Park.
Meanwhile, Pilgrims trio Damien McCrory, Lloyd Saxton and Luke Summerfield are all expected to be offered new deals but Dan Smith has been released after making just two first team appearances this campaign.
"At this stage of his career, I feel Dan needs to be playing
first-team football week-in and week-out and I can't give him that," Sturrock explained.