The Swedish international arrived at the Emirates on loan in January but saw his spell ruined by a back injury, limiting him to just two Premier League appearances for the Gunners.
But Kallstrom claims Arsene Wenger was still impressed with his small contribution to the first team and hinted that he could be back in an Arsenal shirt next season.
He said: “We had a long talk about everything, they were really happy with my work.
“Yes [I might be staying]. We will see what happens. I had a fantastic time at Arsenal and like their style.”
Kallstrom’s claims follows the news that the Gunners are eyeing up a move for a goalkeeper to provide competition for No.1 stopper Wojciech Szczesney next season, with Norwich’s John Ruddy and Reading’s Alex McCarthy thought to be on Wenger’s radar.