The 25-year-old Dutchman has made just 28 appearances since joining from Vitesse Arnhem two summers ago.
Established left-back Patrice Evra last month extended his contract for a further 12 months while United are reportedly interested in Southampton's England international Luke Shaw.
In addition, Buttner does not believe he will get much of a go under Van Gaal.
"Van Gaal never gave me the chance in the Dutch national team, despite being voted man of the match 14 times at Manchester United," he told Dutch newspaper De Telegraaf, although his estimation of the significance of his performances appears to have been inflated somewhat.
"Apparently he is not very confident about me
So I think this is the right moment to leave."
Buttner's agent Alexander Bursac admits remaining at Old Trafford is not really feasible.
"In the past two years, Louis van Gaal has ignored Buttner time after time so what kind of perspective does he have when Van Gaal becomes his new club coach?" he told Voetbal International.
"Patrice Evra signed a new contract and with Luke Shaw they want to buy another player for Buttner's position.
"To stay at Manchester United was not an option for Buttner.
"Dynamo Moscow has great plans for the future and they want to challenge for the title."
Source : PA
Source: PA