The 32-year-old, who has one year left on his Vicarage Road contract, made 27 appearances last season to help the Hornets stay up.
However, the midfielder admitted that he is already in talks with Swiss side Sion and suggested that his next contract may be his last.
Behrami is quoted by The Sun as saying: "I have had discussions with Sion, and there is something serious going on with them. Joining them would be a challenge for me, and I have never yet played in the Swiss Super League.
"I want to play for a club either in or nearer to Switzerland, as I'd like to live in Lugano with my family. I have told Watford that I want to move, and they will decide what happens. But I will accept whichever decision they take, as I get on very well with them.
"I now hope to have four weeks off. I need this time for the sake of my mind and my body, as this last season hasn't been the easiest. The next contract I sign will probably be my last, so I have to give it serious thought."
Behrami, previously of West Ham United, joined Watford from Hamburg in 2015.