Dragic told Tim Reynolds of the Associated Press that Butler suggested last week that physical violence could be coming the guard's way if he didn't re-sign with the team.
"Jimmy's a tough guy. ... I didn't want him chasing my ass," Dragic joked.
The Heat organization also made it known they wanted Dragic back leading up to free agency, surprising him with billboards in his native Slovenia with messages such as, "Your second family is always with you."
"I was in the car with my wife and her brother and they drove me past those billboards," Dragic said. "I didn't know. They told me nothing. They just said, 'Look to the right.' And when I saw myself, saw what they said, it really touched my heart. This is my home. I want to stay here in Miami. I appreciate Pat Riley, Andy Elisburg, the whole organization and what they did for me."