Allen, 31, has become a popular player in Memphis and an important part of their rise to the Western Conference finals this past season.
Allen was named to the NBA's All-Defensive first team for 2012-2013, and received more votes than any other player. He averaged 8.9 points and 4.6 rebounds.
The Boston Celtics made Allen the 25th overall pick of the 2004 NBA draft. In nine NBA seasons, he has averaged eight points and three rebounds.
The Memphis Commercial-Appeal first reported an agreement between Allen and the Grizzlies was in place.
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