Per Pierre LeBrun of The Athletic, Eichel's camp hasn't asked the Sabres for a trade, though the two sides haven't spoken "for a few weeks."
Eichel did hint during a press conference Monday that he could play somewhere else next season.
"I've been a bit upset about the ways things have been handled since I've been hurt," Eichel told reporters. "There's been a bit of a disconnect between myself and the organization. The most important thing now is to get healthy and be ready to play hockey next year, wherever that might be."
The Sabres announced April 15 that Eichel would miss the remainder of the season because of a herniated disk in his neck.
Head coach Don Granato said at the time that the decision about surgery was up to Buffalo's medical staff.
During his press conference Monday, Eichel made it sound like he wanted surgery, but the team prevented it.
"It doesn't work like that. I wish. ... I'm under contract with this team, and they definitely hold a lot of cards on what I can and can't do," he said.
The Sabres signed Eichel to an eight-year, $80 million contract extension in October 2017. The deal runs through the 2025-26 season.
Buffalo selected Eichel with the No. 2 overall pick in the 2015 NHL draft. He debuted for the team that same season at the age of 18, scoring 56 points in 81 contests.
Eichel's final game of the 2020-21 campaign was March 7 against the New York Islanders. The 24-year-old had 18 points in 21 games.
The Sabres finished their season with 37 points, the fewest in the NHL, and a 15-34-7 record.