The Foxes suffered relegation from the Premier League last season and a host of players have left the club this summer.
Versatile full-back Castagne has been targeted by multiple clubs around Europe and the Belgian is willing to move clubs as well.
Fulham are trying to add at least another full-back before the transfer window shuts down and they have identified Castagne as a top candidate.
It has been suggested that Fulham have agreed on a deal worth £15m including add-ons with the Foxes for Castagne.
And according to Belgian journalist Sacha Tavolieri, the Belgian will attend his medical this morning to become a new Fulham player.
It has been suggested that the 27-year-old has agreed a four-year contract with Marco Silva’s team.
The Craven Cottage outfit are expected to announce Castagne’s capture on Tuesday.