The 22-year-old Chelsea winger spent the entirety of the recently-concluded season in Germany on loan with Bayer Leverkusen.
He struggled to live up to expectations in Germany, as he played in 21 matches and only managed to register one goal and one assist.
He is scheduled to be back at Chelsea in the summer and the club will look to get some money for the out-of-favour winger, who has only one year left on his deal.
Nottingham Forest are interested in Hudson-Odoi, but they face competition from Lazio, according to Italian radio station Radiosei.
It has been claimed that Maurizio Sarri and club president Claudio Lotito identified Hudson-Odoi as a potential winger option in a recent meeting.
It is suggested that Hudson-Odoi would cost around €12m to sign from Chelsea and the presence of Sarri at Lazio could smooth the deal.
It remains to be seen whether Lazio could come out on top in a battle with Nottingham Forest for Hudson-Odoi.
