Fyvie is regarded as one of the best young talents to emerge in Scotland in recent years after breaking into the Aberdeen side as a 16-year-old.
The likes of Blackburn and Newcastle have been linked Fyvie in the past, but Fulham are hoping to steal a march on their rivals by luring him to Craven Cottage.
Fulham have held a long-term interest in the 18-year-old and have now firmed up their interest with an offer.
Fyvie, who has recovered from a cruciate knee ligament injury that blighted his season last term, holds the record for the youngester ever goalscorer in a SPL match.
Aberdeen are reluctant to lose Fyvie, but know they will struggle to reject a sizeable offer for the midfielder.