Norwich chief executive David McNally also admitted that the club wanted to keep Steer.
"Jed is an excellent young keeper with a bright future ahead of him, and was very much part of our plans for next season," McNally said.
"We offered him a good 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 during his time at Norwich.