Moore cost £3.5m ($5.42m) when he moved from Aston Villa two years ago after an initial loan spell.
He helped the Baggies gain promotion back to the Barclays Premier League last season but has slipped down the pecking order.
Albion technical director Dan Ashworth said: “We’ve had some interest in Luke but not a firm offer.
“Luke played a big part for us at the start of last season.
“For one reason or another, maybe after Christmas, we changed our shape.
“Ideally we want to get him out on loan and I’m sure we will. For Luke’s career, he would like to go out and get some football.”