The English club offered €1m for a loan with an option to buy Florentino, 21, for €18m next summer.
Benfica considered the proposal for a few days before turning it down, deeming the amount offered too low.
However, the Eagles left room for further talks and it’s likely that Fulham will be back in a few days.
The basis of Fulham’s second offer will be the same, a loan plus purchase option, but they will offer more.
Florentino has been used by Jorge Jesus in preseason, but the excess of midfielders at Benfica means he can leave.