Gordon is facing a minimum one-year ban for failing an offseason drug test, and also was arrested for a DWI this offseason. His hearing in front of commissioner Roger Goodell is set for Aug. 1.
On the team's first day of open training camp practice, Gordon got very little time with the starters.
"The league prohibits us from commenting on these situations," Haslam said Saturday. "I'll say this. First and foremost, we care about our players and want our players to take care of themselves and make good decisions, and we're going to do everything we can to support [them].
"At the same time, the players have to understand they're accountable to themselves, to their teammates, to the front office, and to our fans. People have to understand that, and I'll leave it at that."
Asked if releasing Gordon was ever an option, Haslam simply said, "No."
Haslam also said the Browns "expect better" than they got from rookie quarterback Johnny Manziel this offseason, when photos of him partying were Internet staples.
"I think Johnny said it well," Haslam said. "He made some rookie mistakes. The really great athletes make their news on the field, not off the field. Hopefully Johnny can look at guys like LeBron [James] and [Tom] Brady and Peyton [Manning] and [Derek] Jeter and pattern [himself] after those guys who make their news on the field, not off the field."
Did the message sink in?
"We'll see," Haslam said.
Haslam did not want to get into it much more, though he did add: "We expect better from him."
Manziel said that he can learn from the players Haslam mentioned.
"I'm sure they all made their mistakes at 21, 20 years old when they first came in the league," Manziel said. "But what I take away from that is you learn from the best, and you learn how those guys have carried themselves, which is extremely well on and off the court. I absolutely agree with Mr. Haslam that I can learn from guys like that."
Manziel again addressed his off-field activities, and explained it by saying he has the greatest life he can imagine and he wants to enjoy every second.
"Here's the thing that I want to say," Manziel said. "The reason that I'm popular and the reason that people follow me and there's been such a buzz around me is when I went out on Saturdays at Texas A&M I played with an extreme amount of passion and I played with my heart on my sleeve.
"But more than anything, I had fun. I have fun playing this game. I have fun going out on this field playing football. It's what I live for. It's what I do. The same way off the field. Whether I'm going out and playing golf, whether I'm going out and having a nightlife, whatever it is I have a lot of fun. That's what my life is. And luckily for me I'm living out my dream of playing in the NFL having a ton of fun.
"My dream has come true and [I] finally got some time to get some downtime and celebrate that with my family, with my friends. This is the greatest life that I could have ever imagined for me, and I'm loving that.
"Will I continue to get better being a professional and learn lessons about life? Of course. I'm 21 years old. And age is not an excuse, but I need to mature, and I have done some immature things. But moving forward I'm going to try and mature and get better at handling myself as a professional.
"That's really all I can say about that."