The Baggies had an undisclosed bid, believed to be in the region of £2m, rejected by administrators Duff & Phelps at the start of the month.
However, Roy Hodgson has now refused to deny that the club have launched another bid to capture the Scotland international.
When asked if West Brom had submitted a bid, the 64-year-old replied: "That might be so.
"It's not really my department, it's sporting director Dan Ashworth you'd have to ask about that."
Hodgson is also believed to be interested in Gers keeper Allan McGregor.