However, Parlour cannot see Bilic making such a swift return to management, after being let go by West Ham.
The former Arsenal midfielder said: “Bilic has been mentioned, which I’d be amazed. I can’t see that.”
Bilic’s management style would be a huge change from Pulis’, if he was to take charge at West Brom.
Bilic was considered to be too relaxed in training by some of his critics at West Ham, which is in stark contrast to Pulis’ disciplined style.
West Brom have also been linked with the likes of Ronald Koeman and Sam Allardyce, as they look to find a replacement for Pulis.