Incognito was suspended indefinitely after making a number of racial slurs and threats towards Martin, but the guard claims that the latter sent him similar texts and that the language used was just the nature of their relationship.
Ross now plans to meet Martin face-to-face before dealing with the situation, but he admitted that he was taken aback by the offensive terms being reported.
"I was appalled. I think anybody would be appalled. When you first read that text that was reported, to me I didn't realize people would talk, text or speak that way," Ross told reporters.
"I'm going to meet with Jonathan Martin face to face and hear what he has to say. Then, I will deal with it from there. So much has been said about a lot of different things.
"There will not be any racial slurs or harassing or bullying in that workplace, in that locker room and outside that locker room."
The Dolphins suffered another setback in their season last night when they lost 22-19 to the previously winless Tampa Bay Buccaneers.