Lukas Podolski wants to return to Arsenal when his loan expires at Inter Milan, according to manager Roberto Mancini.
Neil Redfearn has taken heart from Leeds' claims that their young first-team players will not be sold in the summer.
The 25-year-old, who joined the Canaries from Wolves in June 2010, is now tied to Norwich until 2015.
Surman told Canaries Player: "It feels great. It's an honour for me to sign another contract at Norwich City. I've really enjoyed my time here and I'm looking forward to another three years at the club.
"It has been amazing. Everyone keeps talking about these last three years at the club, winning two promotions and then staying in the Premier League."
Norwich are now managed by Chris Hughton, having lost Paul Lambert, the man who took them from League One to the Premier League, to Aston Villa.
And Surman is looking forward to working with the former Birmingham boss as Norwich look to build on last season's 12th-placed finish.
Surman added: "We've a new manager coming in now, and it's a great time to build on what we did last season.
"Everything I've heard about the new manager is really good.
"He's a football man, and a good man manager too. I haven't met him just yet, but I'm looking forward to it as all the lads are. It's going to be an exciting time next season."
Hughton told canaries.co.uk: "Andrew did really well for Norwich last season and as manager I am pleased that he has accepted our offer of a new three-year deal.
"Since joining from Wolves he has continued to improve, and showed this by scoring some important goals in the Premier League last season.
"It's a deal that is well-deserved, and hopefully he can pick up where he left off when we get back for pre-season."