The 25-year-old arrived at Old Trafford during the summer of 2012, but with Patrice Evra ahead of him in the pecking order, the Dutch defender has been restricted to just 28 appearances in all competitions.
His starting opportunities are expected to be even more limited next term as United are thought to be in the market for either Luke Shaw or Daley Blind, both of whom play in the same position as Buttner.
As a result, Buttner's agent has revealed that his client's switch to the Russian capital is nearing completion.
"The owner wants to take the club to the next level. I am convinced that the club can mount a title challenge and qualify for the Champions League," Alexander Bursac told De Telegraaf.
It is believed that Buttner will sign a three-year contract with Dynamo.