While Albion remain in pole position to snap up free agent Reid, they could face stiff competition from their Black County neighbours should Wolves boss Mick McCarthy show an interest.
McCarthy is known to be a big fan of the London-born star and, as Reid recently revealed, the feeling between the two is mutual.
"I was just a schoolboy at Millwall when Mick was there, but he gave me my debut for Ireland and took me to the World Cup eight years ago," explained Reid.
"So I've got great admiration and great respect for him as a manager and as a person. I've got a lot to thank him for throughout my career. He's done a great job at Wolves in helping them stay up this season.
"They had a couple of behind-closed-doors games up at Blackburn this season and I had a catch-up there and he gave me some advice on a few bits and pieces.
"It was a good catch up and I was delighted to see Wolves doing so well this season."