The West Brom captain handed in a written transfer request last week.
Fulham had a £2million plus winger Hameur Bouazza bid rejected and the offer was criticised by West Brom chairman Jeremy Peace.
“I think it’s sad when people make those sort of comments because I can assure you the offer was by no means derisory,” said Hodgson.
“We made an offer for Jonathan Greening. Information through his agent is that he would be very keen to come and join us, but at the moment there’s an impasse between West Brom and us.
“It may not have been the type of offer they were looking for, that’s another matter, but I think to use the word derisory is very strong.
“I know what the offer was and I think for a player of 30 years of age, who’s in the Championship looking to get back into the Premiership, it was anything other than a derisory offer.
“I’m hoping that there will still be some dialogue between the two clubs, because I do know that Jonathan will be very keen to join us and he will be a good addition to our squad with his experience and quality going into the season we’re going into.”
