Hodgson is keen to improve his attacking options before Tuesday's deadline and has been linked with a move for Pogrebnyak.
The Russia international is out of contract at the end of the season, but Hodgson is not planning an imminent swoop for the 28-year-old.
"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."
