The 25-year-old midfielder has been heavily linked with a move away from Germany this month, as he enters the final six months of his current deal.
Gunners boss Arsene Wenger is a long-term admirer of the Swiss born Bosnian-Serb, and was rumoured to be interested in bringing him to the Emirates Stadium.
However, any hopes Arsenal may have had of securing Kuzmanovic's signature have been dealt a blow, after he hinted that he would like to return to Italy, where he previously plied his trade with Fiorentina.
"My relationship with Stuttgart is very good, but I am out of contract at the end of the season," he told Tuttomercatoweb. "And, we have not discussed the possibility of a new deal.
"In regards to the future, I have a clear idea. I want to come and play in Italy once again because I know the language and I like the type of football they play."
Kuzmanovic enjoyed two-and-a-half years at the Stadio Artemio Franchi, before he made the £7million switch to the Bundesliga in 2009.
In the past three seasons, he's made 95 appearances for Stuttgart, scoring 17 goals, but feels it's now time to move on.