The left-back joined the Russian club from Manchester United in 2014 and he was initially a key member of the starting lineup at the Arena Khimki.
However, Dynamo's ongoing financial problems has meant that a number of imports, including 27-year-old Buttner, have been sidelined.
As a result, the Dutchman's representative Alexander Bursac has conceded that Buttner has decided to move on, having seen a move back to the Premier League fall through in the summer.
"Dynamo asked £4m for Alex in mid August, but that was too much for a Premier League club and another in the Bundesliga," The People quotes Bursac as saying.
"By then most clubs had completed their transfer business. Alex didn't want to cancel his contract just like that, as he had signed a good deal until 2017. But now it is a matter of him getting a move in January.
"Alex is not being put under pressure, but Dynamo can't any more offer the big contracts it gave out previously. So we are getting signals that they no longer count him among their important players. The intention on both sides is to find a solution in January."
Buttner made 28 appearances during his stint with United, from which he scored two goals.