Slauson rolled into Cushing, who tore his left anterior cruciate ligament in the second quarter of the Texans' 23-17 win Monday night. Cushing was placed on injured reserve Wednesday.
Another person with knowledge of the situation told The Associated Press on Thursday that Slauson will appeal the fine. The people spoke on condition of anonymity because the league doesn't announce fines until Fridays.
Fox Sports first reported the fine for the hit, which both Slauson and Jets coach Rex Ryan have defended as being legal. Slauson said Wednesday he thought it "would be a surprise" if he were fined.