Agent Rick Smith told ESPN that Martin is doing very well but wouldn't say when his client would return to the team.
ProFootballTalk.com, citing multiple league sources, reported Wednesday night that Smith called Dolphins general manager Jeff Ireland before his client left the team Oct. 28 and complained about the manner in which the second-year player was being treated by Incognito.
In response, Ireland suggested Martin respond to Incognito physically and specifically mentioned that he should "punch" the veteran guard, the sources told ProFootballTalk.com.
Representatives for Martin have turned over evidence of harassment to the Dolphins, the NFL and the NFL Players Association.
Commissioner Roger Goodell appointed attorney Ted Wells to direct an independent investigation into the Dolphins' workplace conduct. That report will be made public.
Martin's family has hired attorney David Cornwell to represent Martin's legal interests in the issues with the Dolphins.
The hiring was earlier reported by Fox Sports. Cornwell released a statement Thursday night on Martin's behalf.
NFL Players Association executive director DeMaurice Smith released a statement Thursday saying he's been in contact with Miami players.
"I continue to be in touch with players in Miami, their representatives and player leadership, and I look forward to information that defines the full scope of the NFL's investigation," he said. "Every NFL player should expect safe and professional working conditions. The NFLPA has taken steps to ensure that every one of our affected members is represented. It is our duty as a union to learn the full facts, protect the interests of players involved and hold management accountable to the highest standards of fairness and transparency."
On Wednesday, veteran Dolphins players offered overwhelming support for Incognito while also displaying anger toward Martin, who left the team after claims of harassment and misconduct.
"I think if you have a problem with somebody -- a legitimate problem with somebody -- you should say, 'I have a problem with this,' and stand up and be a man," offensive tackle Tyson Clabo said. "I don't think what happened is necessary. I don't know why he's doing this, and the only person who knows why is Jonathan Martin."
Oakland Raiders offensive coordinator Greg Olson, who coached Incognito in St. Louis, said Thursday he had spoken this week with Incognito.
"He felt it was taken out of context so he felt like he had a good relationship in that locker room with not only the player in question, but most of the players in the locker room," Olson said of Incognito.
Multiple sources confirmed to ESPN on Monday that Incognito used racial epithets and profane language toward Martin on multiple occasions. In a transcript of a voice mail message from April, Incognito referred to Martin as a "half n----- piece of s---," and added, "F--- you, you're still a rookie. I'll kill you."
Some Dolphins players were aware of the contents in the voice mail, but many defended Incognito against claims that he is racist and intended to harm Martin.
"If I'm not mistaken, this is the same guy [Martin] who was laughing about this voice mail at one point and time, first of all," receiver Brian Hartline said. "Second of all, I believe that, if you go through the whole voice mail, there's some things said that you probably shouldn't say in general, friends or not friends. But I know for a fact that I've said things to my friends that I kind of wish I never said, either.
"With that being said, I never thought it was a death threat. I never thought he was actually going to do the things he said. If you can't take validity from one part of the voice mail, how do you take validity from the whole voice mail? You can't pick and choose what parts count and which parts don't count."
Asked to clarify whether Martin laughed at the voice mail, Hartline hedged.
"I just remember it was being passed around at one point as a joke. I could be mistaken."
Dolphins players described Incognito and Martin as good friends. Quarterback Ryan Tannehill even described Martin as a protégé of Incognito.
"Richie said, 'Jonathan is like my little brother,'" Tannehill said of a past conversation. "I think that's an accurate depiction. He gave him a hard time. He messed with him. But he was the first one there to have his back in any situation."
ESPN.com Dolphins reporter James Walker and ESPN.com Raiders reporter Paul Gutierrez contributed to this report.