The 27-year-old has recently been linked with the likes of Inter Milan and Tottenham.
The Sloevenia international is rated as one of the best goalkeepers in European football.
“There has been no contact for him,” said Gino Pozzo, son of Udinese owner Giampaolo.
“He won’t be leaving for now because he is an important element for our project.
“Obviously, we intend to respect the player’s desire, but we want him to stay.
“How much would he cost? He doesn’t have a valuation.”