The Cottagers have held talks with Benfica over the deal for the midfielder.
Fulham are offering around £2m for a loan fee with the option to buy the midfielder for £25m.
The newly-promoted Premier League club have signed two players from Southampton, with Mario Lemina joining on a season-long loan, while Harrison Reed has joined on a permanent basis after spending last season on loan at Craven Cottage.
The 20-year-old is a traditional central midfielder but Scott Parker could make the best use of his exciting style of play by using him in advanced roles.
He fell out of favour towards the end of the season, and therefore an exit could be on the cards this summer.
Leeds interested but they may have moved on
Back in July, it was reported that Leeds were heavily interested in signing him.
The Whites were very serious about the deal, and they held a discussion with the player’s representatives.
However, it seems Leeds have cooled their interest in the higly-rated young midfielder.
Leeds have already signed Rodrigo from Valencia on a club-record deal, while they are also in talks to sign De Paul from Udinese.