The 27-year-old goalkeeper has attracted Premier League interest with a string of fine performances but appears set to stay with the Serie A outfit for the foreseeable future
The 27-year-old has become a key player for the Serie A team and helped them qualify for next season's Champions League with a third-placed finish.
His performances have alerted a number of clubs with both Tottenham and Inter linked with a move for the shot-stopper.
However, Udinese chief Carnavale has ruled out the sale of both Handanovic and 21-year-old Colombian forward Luis Muriel this summer.
He told Radio Kiss Kiss: "Neither of them will leave - the goalkeeper is still with us."
Handanovic, who joined Udinese in 2004, is the current holder of the Slovenia No.1 shirt and has 57 international caps to his name.