Cut by the Texans earlier this month, Foster is still recovering from the ruptured Achilles tendon he suffered in an October loss to, of all teams, Miami.
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Rapoport tweeted that Foster "could pass a physical now," but the 'Fins are unlikely to sign him until he can go full-speed. Tuesday's meeting will serve as an introduction, while putting the wheels in motion for when Foster is ready to roll later this spring or summer.
The four-time Pro Bowler has been jogging since January and increasing his workouts daily at a Houston-based training facility owned by his brother, Abdul Foster, who recently told the Houston Chronicle: "Arian's doing great."
Foster planned all along to focus on his rehab and slow-cook free agency until he was ready to find a team that suited him.
The Dolphins have second-year back Jay Ajayi on the roster, but their failed pursuit of Denver's C.J. Anderson and Arizona's Chris Johnson signal Miami's desire to import a veteran presence to play in what new coach Adam Gase hopes will be a "stable" of backs.
Foster's rash of injuries turned last season into a wash, but coaches and general managers haven't forgotten how powerful he looked for stretches in 2014. If the Dolphins don't land him, somebody will.