According to Adam H. Beasley of the Miami Herald, a source said there is "legit interest on both sides," but nothing is imminent.
Beasley added that the Dolphins are one of "more than a half-dozen" teams in the running to sign Breeland after recently bringing him in for a free-agent visit.
Omar Kelly of the Sun-Sentinel reported Monday the Dolphins were "actively and aggressively" targeting a starting cornerback.
Xavien Howard is currently locked in as a starting corner with Bobby McCain in the other spot, but Beasley noted the Dolphins would prefer to have McCain operate in a nickel role.
The Dolphins also have 2017 third-round pick Cordrea Tankersley in the mix.
Breeland represents a unique case in that he's a starting-caliber cornerback who is still on the market because of a failed physical. He previously agreed to a three-year, $24 million contract with the Carolina Panthers that was later rescinded because of a foot infection.
Last season, Breeland registered 47 tackles, a career-high 19 passes defended and one interception in 15 games. Over 60 career regular-season games, he has eight interceptions.
If Miami signs Breeland, he will join a secondary that ranked 16th in the NFL last season with 225.2 passing yards allowed per game and 23rd in passing touchdowns allowed with 26.