The Armenian striker netted 21 times in 34 games for the Moscow outfit last term, and has not ruled out a move to the Premier League.
"I've heard there may be some interest in England and Germany," Movsisyan in quoted as saying by the Daily Mail. "I've proven I can score goals wherever I have played and I have been lucky to do so again this year with Spartak.
"It wasn't the season that we wanted but we have a quality group. I'm up for a challenge and always want to test myself against the best.
"If an offer is made for me, I can't control the outcome. Spartak know my ambition and all parties need to be satisfied. Either way, I want success on the field."
Leicester City are the latest English team to be credited with an interest in the 26-year-old.