A league source told ESPN NFL Insider Adam Schefter that the Ravens tried to trade Leach but were unable to find a taker. His agent, meanwhile, told a Houston television station that his client would like to return to the Houston Texans.
Leach is scheduled to visit the Miami Dolphins on Wednesday, a league source told Schefter.
Leach was an integral part of a running game that helped the Ravens become champions last season. Paving the way for standout halfback Ray Rice, Leach made the Pro Bowl in each of his two seasons with Baltimore and was a key figure in the locker room.
"He played a significant role in helping us get to the AFC Championship Game in 2011 and win the Super Bowl last season," general manager Ozzie Newsome said. "He added to our toughness and will to win. Plus, he provided leadership."
After negotiations between Newsome, Leach and the player's agent reached a standstill, both sides agreed it would be best to terminate Leach's contract. But Newsome left open the possibility that Leach could return if he fails to find an adequate suitor in the free-agent market.
"We could revisit this before or during training camp," Newsome said.
Leach's agent told KRIV-TV in Houston that the Texans, who Leach played for from 2007-10, are at the top of the fullback's wish list and he would reach out to the team soon to see if they are interested.
"Obviously, which teams you have the best fit at," agent Ralph Vitolo told KRIV-TV. "The most logical fit and the smoothest transition to another team would be Houston because he's already been there.
"He understands the coaches, the scheme. He's worked with Arian Foster and the rest of the offensive line, so it would be a very smooth transition to go back to Houston."
It is unknown if the Texans, who signed veteran fullback Greg Jones earlier this offseason, would be interested in signing Leach.
Baltimore began a three-day mandatory minicamp Tuesday without Leach, who ran 21 times for 67 yards and one touchdown while with the Ravens. He also had 36 catches for 212 yards.
"Vonta's been as much the heart and soul of this team as anybody since he's been here," coach John Harbaugh said. "He's been a great leader. He's been a tremendous performer. I've never had more fun with a player since he's been there.
"He's just a great guy, and he established us in a lot of ways. He established the personality of our offense as a physical, hard-nosed unit over the last couple years. I wish him nothing but the best, and I'm sure he'll do really well. I'm sorry to see him go."
Leach's departure was a hot topic following the late afternoon practice.
"We're going to miss him on the football field, but I think the tough thing is that you lose out on a friend, a great teammate," quarterback Joe Flacco said. "I'm just going to miss him being around the locker room."
Defensive tackle Haloti Ngata said, "That was weird when I heard about it. He's a monster. He's a great blocker. And it's just going to weird without him. He was definitely a character on our team, and he was a good teammate."
Vitolo told KRIV: "He's probably a fit for four or five teams. Denver, Dallas, Houston, people like that, Cincinnati."
Leach is the latest in a long line of players cut loose or traded by the Super Bowl champs this offseason. The list includes wide receiver Anquan Boldin, safeties Ed Reed and Bernard Pollard, and linebackers Dannell Ellerbe and Paul Kruger.
"It's just part of the business," Leach said of his release. "I have no animosity against the Ravens. They are a first-class organization. They can't pay everybody."
Leach was due to make $3 million this season. The nine-year veteran made the Pro Bowl in each of the past two seasons with the Ravens.
Leach, 31, had indicated that his stint with the Ravens was over in a series of tweets Monday,
"Thanks ravens organization for a great two years," Leach wrote on his Twitter account. "I came here and did what we set out to do and that's win the Super Bowl. My time here is up but what we accomplished, we will be forever linked. Thank the fans for accepting me and my family to Bmore."
In another move Tuesday, the Ravens re-signed tight end Billy Bajema, who played in eight regular season games and four playoff contests for Baltimore last season. Used primarily as a blocking tight end in run situations, Bajema did not have a catch in 2012.
Meanwhile, Pro Bowl right guard Marshal Yanda was a non-participant in the minicamp practice due to an unspecified injury. Yanda dealt with shoulder and knee injuries last season.
Information from The Associated Press and ESPN NFL Insider Adam Schefter was used in this report.