The Birmingham City manager is in talks with the Canaries.
Livermore, who was number two to Nigel Worthington at Norwich, worked with Hughton during his playing days at White Hart Lane and he backed the Canaries' pursuit.
"I think Chris Hughton would be a very good appointment," Livermore told BBC Radio Norfolk. "Chris is bubbly, he is intelligent, he knows exactly what he wants and how he wants his team to play, and he is a great character. He was very well liked at Tottenham Hotspur throughout the many years he spent there.
"The players and supporters - Norwich City have had a fantastic time and it's absolutely brilliant for everybody. Paul Lambert did very well and then obviously finishing where they did, Chris Hughton or whoever comes in as manager - if it is Chris then yes, he has got a hell of a job to follow on.
"But Chris Hughton is very capable of handling that situation. Knowing Chris, it's a big challenge and he would get on with it and cope with it very well."