The Irishman, 27, had been linked with both Blackburn Rovers and Watford earlier this summer, but now appears poised to stay with the Dons for the foreseeable future.
A statement from the club read: "After weeks of intense speculation surrounding Keith's future, the club decided to make its captain available for transfer, with the aim of clarifying as quickly as possible whether Keith would lead the team in the new season.
"With the new season now fast approaching, we feel the time is right to reiterate Keith's position as a Milton Keynes Dons player and allow him to focus on the start of the forthcoming campaign."
Andrews joined the Dons in the summer of 2006 and has scored 21 goals in 85 appearances for the club to date.