Albion's sporting and technical director Dan Ashworth has made initial contact with Rangers to try to lay the groundwork for a deal.
"I know that Dan and I have talked about it," said Baggies boss Roy Hodgson.
"Dan has been in contact with Rangers, but to what extent a bid has been made, I don't know, or what bid has been made I don't know.
"But, yes, Steven Naismith is a player who, when he accepted to reduce his wages, it was fairly obvious he is a player who Rangers might not be able to keep and as a result we are entitled to make an inquiry.
"Whether a bid has been made or turned down, I don't know, but I know Dan has asked about him."