Eichel's agents earlier Wednesday refuted that report, which was made by a Buffalo radio station.
The 20-year-old center will enter the final year of his three-year entry-level contract next season and can sign an extension as of July 1. He could become a restricted free agent following the season.
"I want to be here for a long time," Eichel told the Buffalo News. "That's the way I look at it. I don't want to go anywhere else. I don't want anybody to think that I want to be somewhere else. ... I want to be a Sabre and I want to be a Sabre for a long time and I want to be a part of Buffalo when we win. I know it's an organization that is capable of doing that, and I want to be a part of it and I want to be a centerpiece of it."
The Sabres missed the Stanley Cup Playoffs for the sixth straight season, Eichel's and Bylsma's second with Buffalo. Eichel said his meeting with the media after the season ended could have been handled better and he was not blaming the coach.
"I was frustrated with myself at the end of the year," Eichel said. "I'm not the kind of guy to point the finger at people, and I feel like people are saying that I'm doing that. That's where I get most frustrated and most disappointed. I myself, I need to become a better player. I need to become a better player. I need to become a better teammate, a better leader. I think that's all in the works. You can't do anything but try to iprove yourself, to improve a team. That's the way I look at it.
"Just hearing these things that people are writing after I have a meeting with [general manager] Tim [Murray] and a meeting with Dan, I thought both of them went well. None of anything that I've read so far has been accurate of what was said in those meetings with them. It's a bit frustrating and a bit disheartening because I thought things were heading in the right direction leaving Buffalo. As much as we didn't have a great year, you've got to just look forward to the future."
The Sabres (33-37-12) finished second-to-last in the Eastern Conference, eight points ahead of the New Jersey Devils and 17 points out of a playoff berth. Eichel, who had 57 points (24 goals, 33 assists) in 61 games, returned in December after missing nearly two months with an ankle injury. He was the No. 2 pick in the 2015 NHL Draft, behind Connor McDavid of the Edmonton Oilers.
Murray after the season said he would attempt to start negotiations with Eichel for a contract extension as soon as he was allowed to. Bylsma has three years remaining on his contract.
"The message got across," Eichel said of his meetings with Bylsma and Murray. "I don't think there was any pointing the finger or anything. I think we came together as a collective and said what we think we need to change to be better. I think that's where we left it.
"Tim had voiced his opinions of what he thinks he needs to do, and I said the same thing with mine. I know that Dan did the same thing. As a coach, he said he needs to be better. As a player, I said I need to be better. The same for Tim."
