White, a forward signed after an outstanding season at Iowa State in 2011-12, has been on the inactive list the past four games while feuding with the Rockets over their support for his treatment sessions.
He is being fined for every missed game and failure to meet with a team-appointed therapist, sources told The Houston Chronicle.
White, who has a fear of flying and expected to be able to take a bus to some games, indicated this week he believes the team is using his anxiety issues to deny him playing time.
The Rockets have refused to comment on the situation, the newspaper reported.
The player issued statement saying he believes his "openness" about his condition has caused a backlash from the Rockets.
"This is important to me. It is a health issue," he said. "I must advocate for my rights, it is a player-commodity league -- the failure to meet my requests for support will end with me being unhealthy and that is not a consequence that I am willing to accept to play any sport."