The Baggies have recently been strongly linked with a move for the Russia international.
The 28-year-old’s current contract with Stuttgart is set to expire at the end of the season.
“There will be no moves for Pogrebnyak,” said Hodgson.
“If anything, we’re looking for a striker to drop into our lap. But I’ve got to say the further the transfer window goes the less likely that is to happen.
“It’s not a frantic search – but we haven’t switched off the phones, either!
“It would have to be very much the right type of player that could help us and not just someone who would come in and be another body to deal with.
“It would have to be someone who would stand a very, very good chance of playing and push one of the strikers that have got the shirts at the moment off his perch.
“It’s not an easy thing to do because the quality of our front players is not that bad.”
