The Scottish Sun says they delayed a move for Fyvie last year as he was recovering from a serious ankle injury.
Now Fulham are ready to bid £1million for the player, who is out of contract at the end of the year.
Fyvie, 19, said: "I need to go somewhere else to progress my career. Some people need a change and I feel it's the right time for me to try my luck.
"Some people say I am taking a big gamble but sometimes in life you have to take a risk."