The teenager rose to prominence last season, featuring 16 times for Udinese in Serie A and his form saw many consider him a possibility for Italy's FIFA World Cup squad.
As it was the 18-year-old was not selected by Cesare Prandelli for the tournament in Brazil but Scuffet has still been tipped to become Gianluigi Buffon's long-term successor.
Indeed Scuffet has reportedly attracted interest from a host of teams, most recently from Spanish champions Atletico Madrid who are keen to add to their goalkeeping options after Thibaut Courtois returned to Chelsea after a three-year loan.
However, he has snubbed all overtures and stated his belief that Udinese is the right place for him to continue improving as a player.
"I'm convinced Udinese is the right place for me to grow," he said at a press conference.
"I listened to all the advice and then I took my decision, which I fully believe [is the right one].
"The environment [at Udinese] is great, I love these colours."
Scuffet recently penned a new contract at Udinese that will see him remain with the club until 2019.