Citing a source close to the embattled offensive lineman, the Post reported that Martin, who was at the center of a high-profile bullying scandal this past season, wants to resume his career with another team.
Martin signed a four-year rookie contract with Miami in 2012 worth $4.8 million, $2.9 million of which was guaranteed.
An investigation for the league determined that teammates Richie Incognito, John Jerry and Mike Pouncey engaged in persistent harassment of Martin, another Dolphins offensive lineman and an assistant trainer.
According to the report released this month by investigator Ted Wells, Martin was subjected to "a pattern of harassment" by Incognito, Jerry and Pouncey that included racial slurs and vicious sexual taunts about his mother and sister.
The Dolphins reportedly had considered retaining Martin, a second-round draft selection out of Stanford who started 23 consecutive games before leaving the team in October.
But after meeting with Martin's representatives last week at the scouting combine, the team expects to trade or release the player. Incognito and Jerry are free agents, but Pouncey -- a 24-year-old Pro Bowl center -- remains under contract with the Dolphins.
"How do you take [Martin] back?" the source close to Martin told the Post. "Do you get rid of Pouncey? All these guys talked [stuff] about him. I don't even know how it's possible."
Martin, reached by the South Florida Sun-Sentinel on Tuesday, said he "really can't comment" on what he wants to happen.
"I'm just going to let the process take care of itself," he told the newspaper.
Dolphins owner Stephen Ross said Tuesday that he still plans to meet with Martin, although he said the meeting will not be related to football.
"The owner might believe that what he touches can turn to gold," the source told the Post. "I don't think [Martin] would be open to that."
Ross spoke on a conference call Tuesday to announce his initiative with NYU and the Jackie Robinson Foundation to improve locker-room culture, saying he hopes to lead an effort to eliminate racial slurs, harassment and bullying in sports.
Martin and Ross, who also introduced an anti-bullying bill in sports to Florida's legislature, initially were scheduled to meet in November. But lawyers for Martin and the NFL nixed the idea while the league was conducting its investigation.
"I haven't heard what his feelings are; I've read the [Wells] report," Ross said. "He wants to talk to me as much as [I want to talk to him]. I'm prepared to listen. When you've dealt with something, it's nice to hear from the person directly."
ESPN.com Dolphins reporter James Walker and The Associated Press contributed to this report.