Turner has made 77 appearances for the Black Cats since joining from Hull City in 2009 and he featured 24 times in the Premier League last season.
The centre-half was a regular under Martin O'Neill in the second half of the campaign, but it appears that the Sunderland manager is prepared to let the 28-year-old move on.
He was linked with a return to Hull earlier in the summer, but new Tigers boss, and former Sunderland chief, Steve Bruce, doubted Turner would come back to the KC Stadium.
A deal to remain in the Premier League is now in the pipeline for Turner, who has travelled to Norwich to have a medical.
Canaries boss Chris Hughton is in the market for defensive reinforcements and had also been linked with a move for Birmingham's Curtis Davies.
Hughton is also closing in on a deal for Robert Snodgrass after agreeing a fee with Leeds United for the Scotland international winger.
The Liverpool 2013/14 soccer jersey is available for pre-order. The Reds are eager to compete for silver next season.
Bayern Munich are kings of Germany and hope to be crowned kings of Europe at Wembley later this month!
Chelsea won the Europa League on Wednesday. The Blues defeated Benfica 2-1 on injury time goal from Ivanovic.
One of the top soccer cleats for control the Nike CTR360 will not let you down on the field in tight spaces.
Ajax has released their away soccer jersey for the 2013/14 season. Get in the Gear.
The push for more color on their cleats, adidas has added the infrared colorway to the adiZero f50 Line.
The adidas Nitrocharge is the most talked about new cleat in years. It was released on May 15 and will take your pitch by storm.
Borussia Dortmund hears Wembley Calling and are headed to London for the Champions League final.
The Juventus jersey for the 2013/14 was released earlier this week. Be the first to wear the colors of the Old Lady.
adidas has added some color to the Predator line with this new colorway. Released on May 17. Be the first to own a pair.