The Sweden international is due to return to parent club Spartak Moscow now the Premier League campaign has ended, but remains hopeful a permanent transfer could be on the cards.
Kallstrom made only four appearances during his short stay in London, but the 31-year-old is confident he did enough to convince Arsene Wenger to re-sign him.
"We talked a lot, but of course it stays between us," he told fotbollskanalen.se. "They were very happy with my performance and what I was there to do so it felt good.
"We'll see, it was a very good experience but we’ll have to see what happens.
"I have a year left on my contract in Russia so it is what it is now until something else happens.
"Spartak's a very nice club and I enjoyed working there so it will be a continuation, which is a very good option too."
The 31-year-old joined Spartak in 2012 and has made 30 league appearances for the Russian Premier League club.
