The Manchester United left-back will undergo a medical with the Russian club having found himself left out of the Netherlands set-up under new Old Trafford boss Louis van Gaal
The 25-year-old joined United from Vitesse in 2012 but has largely played second fiddle to Patrice Evra during his time at Old Trafford, making only 13 league appearances over two seasons.
Buttner does not expect that situation to change under new manager Louis van Gaal as he has rarely been selected for the Dutch national team during the former Barcelona coach's time in charge.
His chances of securing first-team football have been further hit by United's pursuit of Southampton left-back Luke Shaw, with whom they have agreed in principle a huge £160,000-a-week contract.
The Dutchman told De Telegraaf: "Van Gaal never gave me the chance in the Dutch national team, despite being voted man of the match fourteen times at Manchester United. Apparently, he is not very confident about me. So I think this is the right moment to leave."
As well as targeting Shaw, United have secured the services of Evra for another season by extending his current contract.
Dinamo finished fourth in the Russian Premier League last season, 12 points behind leaders CSKA Moscow, and will play in the Europa League in 2014-15.
Discussing the Russian club, Buttner added: "But I am convinced that the club now can challenge for the championship and then move into the Champions League."