In a game against the Dolphins, Foster suffered a torn Achilles tendon that ended his 2015 season.
The Dolphins are searching for a running back to replace Lamar Miller, who signed in free agency with the Texans. The team signed C.J. Anderson to a four-year offer sheet, but that bid was ultimately matched by the Denver Broncos.
The Texans did not offer Foster a pay cut before releasing him March 3. He will turn 30 in August and played in only four games last season, hampered by two significant injuries.
He suffered a torn groin in training camp that caused him to miss three games. He returned for four games but then suffered the torn Achilles against Miami.
Since becoming the Texans starter in 2010, Foster has suffered a torn meniscus, multiple hamstring injuries, a knee injury, a back injury that required surgery, a minor groin injury, a major groin injury and a torn Achilles tendon. In that time, Foster has carried the ball an average of 20 times per game, the highest average in the NFL.
ESPN's Tania Ganguli contributed to this report.