The Bears offered $19 million over four years, Mike Klis of KUSA in Denver reported.
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Anderson chose the Dolphins' offer "in large part" because of his familiarity with new coach Adam Gase's offense. Gase set records as Denver's offensive coordinator in 2013 and 2014, and even once referred to Anderson as a "little chubby sometimes."
Miami and Chicago weren't the only teams interested in Anderson after Denver failed to tender him at the second-round level. According to Klis, nine teams contacted Anderson's agent during the NFL's "legal tampering" window last Monday and Tuesday.
The Broncos now have until Tuesday afternoon to match the Dolphins' offer. If they do match, they will make Anderson the third-highest paid running back for the 2016 season after originally offering just $1.671 million on the right-of-first-refusal tender.