Pro Football Talk reported Sunday "all signs currently point to Albert signing with the Dolphins not long after the market officially opens on Tuesday."
Miami heads into free agency with only one starting offensive lineman -- center Mike Pouncey -- signed for 2014. The unit allowed a league-high 58 sacks last season and was partly to blame for a rushing attack that ranked 26th with an average of 90 yards per game.
Albert and/or fellow left tackle Eugene Monroe, who finished '13 with Baltimore, figured to be among Miami's top free-agent targets. The cost for one of the tackles figures to be between $8-$10 million annually.
The Dolphins, who will begin free agency with $35-$40 million in cap space, first tried to acquire Albert from the Kansas City Chiefs on draft weekend last April.
Albert, 29, was Kansas City's first-round pick in 2008 out of Virginia. The 6-foot-5, 316-pounder played his first six seasons with the Chiefs.
NFL teams were free to negotiate with opponents' free agents during the weekend, though players can't sign with new teams until Tuesday.
Last week, Miami re-signed Pro Bowl cornerback Brent Grimes to a four-year deal worth reportedly $32 million ($16 million guaranteed).