Steer is set to link up with former Canaries manager Paul Lambert at Villa when his contract expires on July 1, but Norwich want some financial reward for the 20-year-old's development.
Norwich chief executive David McNally said: "Jed is an excellent young keeper with a bright future ahead of him and was very much part of our plans for next season and beyond.
"We offered him a good new contract, but it looks like he has opted to sign for Aston Villa instead.
"We are obviously disappointed to be losing the services of a very promising young England international keeper and will be seeking substantial compensation from Villa."
Steer made two FA Cup appearances for Norwich in the 2011/12 season, and has also had loan spells with Cambridge United and Yeovil Town.