Kyle, who is out of contract in the summer, flew out to Turkey for Spartak's pre-season training camp to play in a game against Zhemchuzhina Sochi.
The 28-year-old did not score but had a hand in one of the goals in a 3-0 win.
"I've not decided on anything; I've just come out to speak to them," Kyle told BBC Scotland.
"I enjoyed the experience."
Spartak's assistant coach Kazbek Nakhushev this week revealed his side are interested in signing Kyle.