The teenage goalkeeper has won admirers across Serie A with his displays this season but Cristiano Giaretta says the club will not consider a sale this summer
Big things are expected of rising star Scuffet, who has won plenty of admirers since Francesco Guidolin handed him a first-team debut against Bologna in February.
The 17-year-old kept a clean sheet in that match and has made a further 10 appearances in his breakthrough season.
Scuffet's impressive performances have led to talk of a move away from Udine and Giaretta confirmed that there has been contact with Milan.
"There has been a brief meeting, but nothing concrete," Giaretta told TuttoMercatoWeb.
"And as for the future, I can say that he will not be on the market for next season."
Juventus and Italy veteran Gianluigi Buffon believes Scuffet could well force his way into Cesare Prandelli's World Cup plans should his performances continue.
"Should Scuffet go to Brazil? Considering what he is doing I'd say he deserves it, but watch out for Mattia Perin and Francesco Bardi too," Buffon said.