22-year-old Fleetwood was the Blue Square Conference top scorer last season netting 34 goals and the former Cardiff City stiker attracted attention from a host of clubs.
Rovers manager and former Crewe player Jim Harvey told BBC Gloucestershire "My understanding is that Stuart has spoken to Charlton, and I think things are pretty much tied up.
"He's on holiday at the moment and when he returns I believe things will be sorted out one way or the other."
Fleetwood would have to fight for a place at the Valley with Charlton already having former Crewe striker Luke Varney, Chris Dickson, Andy Gray, Chris Iwelumo, Svetoslav Todorov, Marcus Bent and Izale McLeod on their books.