The 25-year-old Dutchman has made just 28 appearances since arriving from Vitesse two years ago, having been signed as cover for Patrice Evra.
However, with France international Evra penning a new 12-month contract recently and United reportedly plotting moves for the likes of Luke Shaw and Daley Blind, Buttner's hopes of a first-team slot look increasingly unlikely.
Buttner believes the impending arrival of Louis van Gaal at Old Trafford also limits his chances, after being repeatedly snubbed by the current Netherlands boss on the international scene.
Buttner told Dutch newspaper De Telegraaf: "Van Gaal never gave me the chance in the Dutch national team, despite being voted man of the match 14 times at Manchester United.
"Apparently, he is not very confident about me. So I think this is the right moment to leave."
Buttner's agent Aleksander Bursac added: "Dinamo Moscow has great plans for the future and they want to challenge for the title."
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