The incident, which also included defensive coordinator Anthony Weaver, took place in the week leading up to the winless Texans' Week 3 loss to the Pittsburgh Steelers, according to ESPN and multiple reports.
Sources confirmed to ESPN that "a verbal blowup at practice" occurred two weeks ago, with one source telling ESPN's Dianna Russini that the incident was when O'Brien "lost the team."
Watt, a three-time Defensive Player of the Year, on Wednesday said he is looking forward to a "fresh start."
"I'm not going to talk about what happened at practice or what conversations were had or whatever it may be," Watt said. "The situation is what the situation is and we ... right now have a fresh start and we had a good practice today and we're looking forward to Jacksonville.
Added Watt: "When you're 0-4, obviously things need to change. I mean, it wasn't working. I appreciate and respect what we had. We won four division titles in six years with Bill and I appreciate that and that time, but obviously this year, we're 0-4 and stuff wasn't working. When you have the talent that we have, specifically at the quarterback position in this league, we can't be 0-4."
Romeo Crennel was named interim coach heading into this week's game against the Jaguars.
Watt said he wishes "no ill will" toward O'Brien.
"The one thing I'll say about Bill O'Brien is he always stood up for his players," Watt said. "... Certainly, he tried to do whatever possible to support his players and give his players the absolute best support. And I truly believe that he always did what he believed was best for this football team. So I don't have ill will at all."
Quarterback Deshaun Watson said what happened to O'Brien was just the "business" of the league.
"I have the [upmost] respect for Coach O'Brien for getting me to Houston, teaching me what he taught me the four years I've been here," Watson said. "The discipline, just everything as a person, getting ready for professional football. He did a lot of amazing things to help me get two Pro Bowls and win the AFC South every year that I've played a full year. So I have all the respect for him and the things, but that's just how the business goes."
ESPN's Sarah Barshop contributed to this report.