The keeper is currently on loan at Twente from PSV Eindhoven, but he has failed to impress the Enschede club's paymasters.
Ten Rouwelaar is in the first season of a two-year loan stint with The Tuckers, but they are happy for him to move on.
"We will co-operate with a move to Zwolle," said Twente technical co-ordinator Johan Plageman.
PSV are unlikely to block a move, which could well result in the youngster signing for Zwolle in the summer.
