The Ivory Coast international joined the Cottagers from Nice for a club record £25 million fee last summer but could be on the way out already following their relegation to the Championship.
Seri has made it clear that he wants to leave, the Express reports, and Milan have declared interest.
However, Fulham are believed to want the same fee they spent on the player 12 months ago, which could stall the Rossoneri’s advances.
Roma are said to be weighing up a move, while Napoli and Inter Milan are also monitoring the 27-year-old.
Seri’s agent Franklin Mala confirmed interest from the Italian capital, saying: "My Italian partner and I spoke to Roma a couple of weeks ago. We'll see how the situation evolves.
"He'd be happy to play in Serie A and Roma are a very good club."
Crystal Palace are also understood to have shown interest in the player, but are yet to follow up an initial enquiry with a concrete bid.
Now read...
QUIZ! How many of Barcelona’s 50 biggest transfers can you name?
OUCH 10 big, disastrous signings who cost managers their jobs
