The former Australian international has turned down an offer of a new contract and may now join Rhinos' rivals, Bradford.
"An offer was put to Chris," said the Leeds' chief executive, Gary Hether-ington. "However, he has not accepted it and wishes to keep his options open."
The loss of McKenna, who arrived as a centre but has proved more successful in the second row, comes after Mark Calderwood's decision to join Wigan.
Leeds' winger Marcus Bai is also being linked with a transfer to Bradford, but Jamie Peacock could move in the opposite direction.
The two clubs are expecting a verdict this week in the court case in which Leeds are accusing Iestyn Harris of breaching an agreement with them by signing for the Bulls.Reuse content