The 22-year-old has returned to West London after enduring a difficult time on loan at German outfit Bayer Leverkusen.
Hudson-Odoi was unable to nail down a place in the Leverkusen side, and as a result, he was restricted to just 14 Bundesliga appearances.
With 12 months remaining on his Chelsea deal, there is an expectation that Hudson-Odoi will leave the club during the current transfer window.
Chelsea boss Mauricio Pochettino cannot guarantee Hudson-Odoi a regular starting place with the likes of Noni Madueke, Raheem Sterling and Mykhaylo Mudryk above him in the pecking order.
As a result, the Chelsea academy graduate is looking to secure a move to a club that can offer him regular first-team football.
According to The Athletic, Fulham have identified Hudson-Odoi as a transfer target, and they have formalised their interest by tabling a bid.
Their initial proposal was turned down by the Blues, but the report suggests that it is likely the Cottagers could return with a second offer.
Marco Silva's side are hoping to bolster their wide options after seeing the likes of Manor Solomon and Neeskens Kebano depart this summer.
Fulham are hoping to keep hold of experienced winger Willian, who is currently a free agent following the expiry of his contract.
However, the Cottagers could be left disappointed, with Nottingham Forest in advanced discussions to sign the Brazilian.
Forest have also been mooted as a potential destination for Hudson-Odoi, while AC Milan are believed to be showing an interest in the Englishman.
After rising through the youth ranks at Chelsea, Hudson-Odoi has gone on to make 126 appearances for the senior side, registering 16 goals and 22 assists.