The former Italy international, who almost retired last season but was persuaded to carry on playing, has refused to say where his future lies but reports claim he is moving to north America.
MLS side New York Red Bulls have been linked with Di Natale, but NASL side New York Cosmos are rumoured to have offered him a deal worth ??6m over two years.
Di Natale has spent his entire career in Italy, coming through the youth ranks at Empoli before joining Udinese in 2004.
The 37-year-old has scored 188 goals in over 350 appearances for the Bianconeri and is the club???s leading goalscorer this season with nine goals.
???I will not renew my contract in June,??? Di Natale told Italian newspapero La Gazzetta dello Sport. ???I will leave Udine.???