Handanovic has established himself as one of Udinese's key players since joining from Domzale in 2004, and is now regarded as one of the best shot-stoppers in Italy.
On the other hand, Milan's recent struggles have led many to suggest it's high time the Rossoneri invest in a quality goalkeeper, rather than constantly rely on veteran custodian Christian Abbiati.
However, Gino Pozzo, son of Udinese president Giampaolo, has now made it clear that Udinese will not be willing to do business with anyone in the January transfer window.
"Samir is making the difference for us," Pozzo told La Gazzetta dello Sport.
"We're calm about the interest of other clubs.
"Traditionally, we don't sell any important players in January."
Udinese face a fight on their hands to keep their best players at the Stadio Friuli, with Alexis Sanchez and Gokhan Inler two big names that the club lost earlier this summer, to Barcelona and Napoli respectively.