In the text, Ross expressed to Martin what he also said in a team news release last week -- that he is committed to creating a professional environment for all members of his organization.
Ross also has spoken to NFL commissioner Roger Goodell about the situation in Miami, as well as with other league officials.
The NFL's independent investigator, Ted Wells, is expected to begin his diligence with Martin, who will become one of the first people, if not the first person, Wells interviews later this week, league sources said. Wells' work will continue with other Dolphins players, coaches and administrators.
Team officials with potentially pertinent knowledge of the situation will be reviewed as the investigation extends beyond players, league sources said.
The NFLPA will act as a watchdog to make sure there's a fair and transparent process for each player who is interviewed.
But it's not just a few players who could be facing consequences; it's an organizational issue that threatens to impact many. And the NFL and NFLPA are doing what they can to make sure no preconceived conclusions are drawn, sources said.
On Sunday, Incognito deflected blame for many of his harsh actions against Martin during an interview with Fox Sports and also accused his teammate of using equally crass language, claiming that was the nature of their relationship.
"When words are put in a context, I understand why a lot of eyebrows get raised," Incognito told Fox Sports during the interview. "But people don't know how Jon and I communicate to one another. For instance, a week before this went down, Jonathan Martin texted me on my phone, 'I will murder your whole f---ing family.'
"Now, do I think Jonathan Martin was going to murder my family? Not one bit. He texted me that. I didn't think he was going to kill my family. I knew that was coming from a brother. I knew it was coming from a friend. I knew it was coming from a teammate."
Martin's lawyer, David Cornwell, responded to Incognito's claim via Twitter on Sunday. The tweet said, "JMart's text 2 Richie Incognito. U decide" followed by an image of a woman holding a dog from a comedy website with the words embedded in the picture, "I will murder your whole f---ing family."
Incognito, meanwhile, staunchly denied bullying Martin and claimed to be Martin's most supportive teammate. Incognito said he was genuinely surprised Martin left the team and that the issue became a national media firestorm.
ESPN.com Dolphins reporter James Walker contributed to this report.