Tranmere rejected a bid of £1.5 million for Koumas at the turn of the year, and Rovers manager John Aldridge is not keen to lose one of his brightest prospects.
Derby County, Ipswich Town and Manchester City were among the Premiership clubs to watch the 21-year-old in recent months, but Fulham are now reportedly ready to approach Tranmere with a bid.
Manager Jean Tigana is said to be preparing a bid of around £2 million for Koumas, which he hopes will finally see him allowed to leave Prenton Park.
However, the player's commitment to the club until 2004 would indicate that he is in no hurry to move to the promotion favourites, and Aldridge is loathe to sell as the club strive to avoid relegation to the Second Division.
Click here to read our earlier story, Palace Will Not Up Bid For Koumas
