Rapoport noted Miami's focus has shifted to Taylor after missing out on Teddy Bridgewater. NFL Network's Jane Slater reported Tuesday that Bridgewater is expected to re-sign with the New Orleans Saints despite having a "bigger deal on the table" from Miami.
Taylor could be Miami's starter in 2019 if he signs since the Dolphins are reportedly expected to release incumbent starter Ryan Tannehill.
Along with potentially signing Taylor, Rapoport noted the Dolphins are looking to select a quarterback in the 2019 NFL draft.
The 29-year-old Taylor spent the first four seasons of his NFL career as a backup for the Baltimore Ravens before signing with the Buffalo Bills. Taylor started for three seasons in Buffalo, going 22-20 with one Pro Bowl nod and one playoff appearance.
Taylor was dealt from Buffalo to the Cleveland Browns last offseason, but his tenure as Cleveland's starting quarterback was short-lived.
The 2011 sixth-round pick out of Virginia Tech went 1-1-1 in three starts before getting supplanted by 2018 No. 1 overall pick Baker Mayfield. In four appearances last season, Taylor completed just 49.4 percent of his passes for 473 yards, two touchdowns and two interceptions while rushing for 125 yards and a score.
While Taylor struggled last season, his most productive campaign came in 2015 when he was named to the Pro Bowl. Taylor completed 63.7 percent of his passes that season for 3,035 yards, 20 touchdowns and six interceptions. He also rushed for 568 yards and four touchdowns.
Aside from his mobility, Taylor's greatest asset is protecting the football. He ranked eighth or better in pass interception percentage in three straight seasons from 2015-2017, and he paced the NFL in that category in 2017, per Pro Football Reference.
If the Dolphins move on from Tannehill as expected, Taylor could be a quality caretaker for the offense until a long-term option is found.
That option could be discovered in the 2019 NFL draft since Miami owns the No. 13 overall pick. The Dolphins may need to trade up in order to get their desired quarterback, but there are some intriguing prospects available, including Oklahoma's Kyler Murray, Ohio State's Dwayne Haskins, Missouri's Drew Lock and Duke's Daniel Jones.
Miami appears to be heading toward a rebuild, but Taylor's resume suggests he is a quarterback who can at least help the Dolphins remain competitive while they piece together a new core.