Garrett, the older brother of Dallas head coach Jason Garrett, does not have a contract with the Cowboys for 2011.
The decision by the Cowboys comes less than a week after they denied the Houston Texans permission to talk with linebackers coach Reggie Herring regarding the same position.
John Garrett joined the Cowboys in 2007 after serving as the University of Virginia's wide receivers coach and assistant head coach. Dolphins head coach Tony Sparano was the Cowboys' offensive line coach in 2007 and got to work with Garrett. Jason Witten has played in three straight Pro Bowls under Garrett, who is seen as a detailed, driven coach.
Dan Henning had been Sparano's offensive coordinator but the two decided to part ways.
If Garrett becomes Miami's coordinator, he would be the second departure on the Cowboys' offensive staff. Wide receivers coach Ray Sherman, whose contract expires shortly, has been told he will not be retained.
Quarterbacks coach Wade Wilson and kicking consultant Chris Boniol are also not under contract for 2011.