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 had alerted the north London rivals, who are reportedly looking for more competition between the sticks for Wojciech Szczesny and Brad Friedel respectively.
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.