The 35-year old Northern Ireland defender is believed to be contemplating a one-year extension with the Baggies as Leicester City circle but club and country teammate Brunt has urged him to stay put at The Hawthorns.
"I'm quite surprised it's in the situation it is. It would be a no-brainer for me," said Brunt.
"He's a guy who plays every week in the Premier League. People keep speaking about his age but if you see him day to day in training he's an extremely fit lad.
"For the age of him he's a bit of a freak really and for him to keep grinding the level of performance he does week in, week out...it's just a no-brainer.
"Ever since he got back in the side around Christmas time he's never looked back.
"He's pretty much been like that ever since he joined the club, so hopefully they get that sorted."