The Switzerland international has been suffering from a recurring toe problem throughout the season.
The 28-year-old underwent tests in Barcelona on Monday and has been given a specific treatment that will be reviewed next week.
"We have pinpointed the problem," Behrami said to sscnapoli.it. "I will do all that I can to avoid surgery.
"I am confident to have a good recovery, led by the Napoli medical staff.
"After 10 days I will be more positive and optimistic."
Behrami, who is set to be included in Switzerland's World Cup squad this summer, has made 14 league appearances for Napoli this season.