Nolan spent the 2009 season directing the Denver Broncos' defense, but the sides agreed to part ways Monday.
The Dolphins had been seeking a replacement for former defensive coordinator Paul Pasqualoni, whom they fired after the season.
NFL.com's Steve Wyche reported Monday that the Dolphins asked the Broncos for permission to speak to Nolan, but it isn't known if that call caused the split. Nolan told The Denver Post only that he and the Broncos had "mutually agreed to part ways," and a team-issued statement echoed that sentiment.
Nolan was 18-37 in three-plus seasons as the San Francisco 49ers' coach before he was fired seven games into the 2008 campaign.
Nolan becomes the third member of coach Josh McDaniels' inaugural staff to depart Denver following a disappointing 8-8 season. Offensive line coach Rick Dennison left for the Houston Texans' staff, and longtime running backs coach Bobby Turner was reunited with Mike Shanahan in Washington. Both Dennison and Turner were holdovers from the Shanahan era.
The Broncos intend to interview outside candidates to replace Nolan rather than promote from within, La Canfora reported, citing a source. Dean Pees, who has strong ties to McDaniels from their New England days, recently decided not to seek a new contract from the Patriots and is a favorite to land the position in Denver.
After being fired by 49ers, Nolan tried his hand in broadcasting but found himself wanting to return to coaching. Then McDaniels came calling, offering Nolan a chance to turn around a Denver defense that had slid under Shanahan.
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Known as a defensive wizard, Nolan jumped at the challenge. He holed up in his office last offseason as he installed a new look and shuffled personnel. The Broncos tried to give Nolan the pieces, bringing in perennial Pro Bowl safety Brian Dawkins to serve as a leader and add a swagger that had been missing.
The Broncos started the season 6-0 and were the talk of the league. Then they went into a free fall, losing eight of their next 10 games to miss the playoffs for a fourth consecutive year.
The Associated Press contributed to this report.