The Gunners have been strongly linked with a move for the 24-year-old, whose contract in Moscow expires at the end of the current season.
However, Sarsania says that the Premier League side have now pulled out of the race, leaving Kokorin's future up in the air.
"I don't know where Kokorin will continue his career," Sarsania told Sport Ekspress. "There was interest on the part of Arsenal, but now there is not."
The Russian international has netted 10 times in 36 games for his country since making his debut in 2011.