There is speculation that the condition of his injured hip could void the deal.
Tuesday's trade included Jae Crowder, Ante Zizic and the Brooklyn Nets' 2018 first-round draft pick going to the Cavaliers for Irving.
There's also the possibility that rather than voiding the deal the Cavaliers could ask for additional compensation such as another draft pick.
Thomas suffered the injury during the playoffs this year and is rehabbing the hip. ESPN reported that he has not begun running.
Celtics general manager Danny Ainge acknowledged that the hip injury played a factor in the Celtics seeking the trade.