New Spartak coach Unai Emery is desperate for reinforcements in the centre of the pitch ahead of the 2012-13 campaign, and he supposedly sees the 27-year-old Diarra as the ideal addition to his squad.
AC Milan have also been credited with an interest in Diarra, but his agent has indicated that the midfielder is leaning towards a move to the Russian capital club.
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"I think it will be hard to see him move to Italy," Claudio Vigorelli told Sportitalia.
"First of all, because he has one more year left on his contract with Madrid.
"And then because he has a good offer from Spartak Moscow."
The Frenchman joined Real Madrid from Portsmouth in January 2009, and quickly became an important first team member at Los Blancos.
However, Diarra has lost his spot in the starting XI under Jose Mourinho, and could therefore be allowed to leave the club this summer.