The 31-year-old struggled with injury after joining the Gunners on loan from Spartak Moscow in January, but he claims that talks with Arsene Wenger have boosted his chances of securing another move to the Emirates Stadium.
"We had a long talk about everything," Kallstrom is quoted as saying by The Mirror. "They were really happy with my work.
"We will see what happens. I had a fantastic time at Arsenal and like their style."
Kallstrom made just four appearances for Arsenal, largely due to a back problem.