Buttner made the move from Vitesse to Old Trafford on a five-year deal last summer but struggled to establish himself as a regular starter as Patrice Evra remained the first-choice left-back.
United were keen to sign another player in Buttner's position during the transfer window but failed to land either Everton's Leighton Baines or Fabio Coentrao from Real Madrid.
Buttner admits that he had been interested in a loan move to Besiktas to ensure he would get plenty of football ahead of the World Cup, but he has now told a Dutch newspaper that he is optimistic of playing regularly following a meeting with Moyes.
"Last year I have had a good season and the club have seen that," Buttner is quoted as saying in De Telegraaf.
"The club now want to talk about a new deal. That shows a lot of appreciation."
Speaking about the possibility of joining Besiktas on loan, the 24-year-old added: "It was a pity that fell through. With an eye on the World Cup next year in Brazil, I wanted to play games.
"Last Wednesday I had a good meeting with our manager David Moyes. He told me that I will play enough this year at Manchester United.
"He absolutely didn't want to let me go. He sees me as a full United player."