The Greek hitman has long been on the radar of Liverpool, who are rumoured to be holding off until the summer before committing to a move.
But, Fulham are ready to push through a deal this month as they look to stave off the threat of relegation.
The Cottagers’ eagerness to thrash out an arrangement has come in the light of AC Milan’s interest in Adel Taarabt, who has developed into a big part of the club’s attacking set-up.
Rene Meulensteen saw a £9.5m offer for Mitroglou rebuffed last week, but has now returned with a £12m bid.
A move for the Liverpool target could also open the door for Dimitar Berbatov to leave.
The enigmatic Bulgarian recently announced that he is keen to leave Craven Cottage, alerting Tottenham.
Fulham are also interested in West Ham’s Ravel Morrison.
Meulensteen worked with the controversial starlet when at Manchester United, and has been buoyed by the player’s desires to move across London to help his side beat the drop.