Wright rocked Arsenal by slamming in a written transfer request last week, which was immediately rejected by the board.
And Rioch told me: "I was surprised when he asked for the transfer.
"But I told him I would recommend that it be turned down, and as far as I am concerned I want him to remain at Highbury for the three years of his current contract.
"To say there is a personality clash between us is absolute nonsense."
But Wright is still adamant that he wants to leave the Gunners.
Rioch has still not signed his own contract with Arsenal nine months after arriving from Bolton. He claims it is merely a question of lawyers dotting the I's and crossing the T's.
Rioch spent pounds 12million at the start of the season on Dutch master Dennis Bergkamp and England skipper David Platt.
But although Arsenal have at least another pounds 15million to spend, Rioch admitted: "I can't see any players joining us imminently, and there is no likelihood of any one going before the transfer deadline."
Rioch insists that there is no conflict between him and his stars. But his admission that Wright could be at Highbury longer than the manager is a clear indication that the pressure is telling.