Traylor started 10 games last season and finished with 33 tackles.
Traylor is a massive run-stuffing lineman who is ideal to play nose tackle in a 3-4. The Dolphins' concerns at that position have to do with the health of Tim Bowens and Larry Chester, both of whom missed almost all of last season because of injuries.
Saban indicated his concern in a roundtable discussion with reporters last week and The Miami Herald reported on Monday that Bowens was contemplating retirement.
In addition to Denver and New England, Traylor also has played for Green Bay, Kansas City and Chicago. He was given number 94 by the Dolphins.