The Sweden international is expected to bring an end to his eight-year stay in France, with a move to Russia believed to be on the cards once he completes his physical
The Sweden international has been at Stade Gerland for the past five seasons, making more than 170 Ligue 1 appearances for les Gones, having joined in 2006 from fellow French side Rennes.
The 29-year-old was one of the four players earmarked by club chairman Jean-Michel Aulas who he wants to see leave the club, with the Coupe de France winners willing to sell.
Kallstrom was expected to depart for Rubin Kazan last summer, but a move failed to materialise. Instead, Russian Premier League rivals Spartak Moscow, now under the stewardship of Unai Emery, looks set to snap up his services.
According to the report, Kallstrom was preferred over Galatasaray midfielder Felipe Melo, with the Swede likely to cost around €3 million.
The Lyon man is expected to undergo a medical either on Saturday or Sunday ahead of his move to Russia.