The Cottagers walked away from discussions with their west London rivals just over a week ago due to Chelsea’s £8million asking price, but have since returned to the negotiating table.
Hudson-Odoi now faces a dilemma regarding which club to choose. He has agreed personal terms at Craven Cottage but Forest are led by his former England youth coach Steve Cooper.
Fulham already beat their Premier League rivals in a battle to re-sign Willian after Forest attempted to hijack talks in July.
Hudson-Odoi has been training with Chelsea’s Under-21s for the last two months and is considered surplus to requirements at Stamford Bridge.
Fulham are also in talks with Everton over a potential £20m deal for Alex Iwobi, who has just one year left on his contract at Goodison Park.
The former Arsenal star's arrival could see midfielder Harrison Reed join Wolves, who have asked for the terms required to make a move. Reed is open to leaving Fulham having been guaranteed an important role at Molineux.
Fulham boss Marco Silva is keen to add even more players to his squad, with a striker to replace Aleksandar Mitrovic also sought after. A move for Sevilla’s Lucas Ocampos collapsed on Wednesday as he refused to sign despite the two clubs coming to an agreement on a £15m fee.
Fulham are also looking for an additional full-back despite signing Leicester’s Timothy Castagne for £15m last week. AC Milan’s Fode Ballo-Toure, Union Berlin’s Josip Juranovic and Southampton’s Kyle Walker-Peters were previously sounded out.