Roy Hodgson's side have already had a £1.5 million bid for the Ayrshire-born player knocked back and Rangers' administrators Duff and Phelps are currently mulling over an improved offer of £2.5m.
The player is currently recuperating from damaging his cruciate ligament last autumn, but Gray said: "My advice to those making the decision at The Hawthorns would be to do whatever they can to make it reality.
"I don't think Roy Hodgson's pursuit of the midfielder has been a secret, the Baggies have had a couple of bids for him knocked back in recent weeks.
"But if we are led to believe what we read then the two clubs are a lot closer to sorting something out and I, for one, think it would be a brilliant bit of business. I have seen a lot of him over the years and the one thing I have never doubted is whether he could cut it in the Premier League – of course he could. At 25 he is in his prime."
Meanwhile, Gers boss Ally McCoist has passed his best wishes on to Trevor Francis after the one-time Ibrox star suffered a heart attack.
Francis, the 52-times capped England player, was taken into hospital on Friday and is said to be comfortable after surgery.
He spent a little over a year with Rangers winning the League Cup in 1987/88 when Aberdeen were beaten on penalties.
McCoist said: "It was a shock to hear of his heart attack but he is a fighter and I hope he can make a quick and complete recovery."