The Dolphins completed interviews with in-house candidates Dowell Loggains and Darren Rizzi on Friday but the team is now zeroing in on Flores for the job.
Flores has been a member of the Patriots' coaching staff for 11 seasons and spent the past three years specializing with the linebacker unit. He took over defensive play-calling duties after former defensive coordinator Matt Patricia left to become head coach of the Detroit Lions last offseason.
The Patriots ranked 21st in total defense this season and seventh in points allowed per game.
The Dolphins and Cincinnati Bengals are the only teams yet to name a new head coach. The Bengals reportedly want to hire Los Angeles Rams quarterback coach Zac Taylor for their vacancy when L.A.'s postseason is concluded.