The 33-year-old's current deal is due to expire at the end of next season and the club have opened talks with him over a potential extension.
Brunt believes the Baggies should sort out his fellow Northern Ireland international's future sooner rather than later, insisting he has been "massive" for the club this season.
"I can't speak highly enough of him as a lad, or of his performances on the pitch," Brunt told the Express & Star.
"He's a good friend of mine as well so I would love him to stay, and hopefully the club will sort it out.
"He's been massive for us. From day one, since he stepped into the team, he has been our most consistent player.
"And that's coming from someone who had never played in the Premier League until he was 31.
"I had known him for a long time and I knew he was a good defender. But when it came to the Premier League it was as unknown for me as it was for everybody else, and probably to him as well.
"But he has stepped up and been fantastic for us."