The French international is held in high regard across the channel but, even so, has struggled to adapt to life at Marseille, whom he joined from Lorient in 2011.
His younger brother, Romain, already plies his trade in the Premier League with Francophiles Newcastle United and Morgan is keen to test himself in England.
Predominantly a right winger, Amalfitano can also play behind the striker or in central midfield.
Marseille would be happy to sanction a transfer but are thought to be less willing to let the midfielder go temporarily. Fulham are thinking differently, though, and would rather take the lesser risk and bring the Frenchman in for a season, with the option to sign him up permanently.
Versatility is one of Amalfitano's biggest assets, but he is also a good passer of the ball and can provide the creativity that has been so lacking in the Fulham squad of late.
But whether a deal is likely to happen is an entirely different matter. L'Equipe have linked us with the Marseille player recently too, but a right winger is by no means a necessity at Craven Cottage. Ashkan Dejagah is currently filling that hole and doesn't look like letting his first team spot go with ease.