Dempsey and his representatives have been in conversation with the west London club for the last week as he aims to try and secure some regular football during the MLS off-season.
The USA international will have to wait until January 1 to confirm the move and the Cottagers are expected to face competition with West Ham also considering making a move.
The MLS season gets back underway on March 8 and the Premier League outfit will be eager to keep hold of him until late February as they aim to avoid relegation.
The 30-year-old spent five-and-a-half years at Craven Cottage and netted 50 league goals before joining Tottenham and eventually returning to his homeland.
Fulham last week