"It's all good. It's just part of the business," Cushing told the newspaper in a text message when asked about the news.
Last season, before the Texans' Week 2 game, Cushing was suspended for 10 games for violating the NFL's policy on performance-enhancing substances. He was previously suspended four games for violating the same policy in 2010.
Cushing signed a six-year, $52.5 million contract in 2013, but all the guaranteed money in his contract was paid after the 2017 season. He was scheduled to be paid a base salary of $7.25 million in 2018.
In five games last season, Cushing had 16 combined tackles, 1.5 sacks and one tackle for loss.
Before the Texans' final game of the season, Cushing was asked if he expected to return to Houston in 2018. The linebacker said, "I don't know. I'd like to."
The 30-year-old said he wants to continue his career even if he isn't playing for the Texans.
In nine NFL seasons, all with the Texans, he has 674 tackles, 13.5 sacks, eight interceptions and nine forced fumbles in 104 games.
ESPN's Sarah Barshop contributed to this report.