Hodgson was reported to be considering a move for former England centre-back Woodgate, who is available on a free transfer following the expiry of his Tottenham contract, but he has now dismissed the speculation.
He told the club's official website: "There is no truth in the Woodgate rumours."
Meanwhile, Hodgson could lose left-back Shorey this summer, with the 30-year-old left-back keen to return to Forest after a successful loan spell in 2009-10.
"I'll be very sad if Nicky comes banging on my door because he wants to leave West Bromwich Albion to go to Forest," Hodgson said.
"I've got great respect for Forest. I think they are going to be a major force next year but, at the moment, I can offer Nicky Shorey Premier League football and I hope that's what he'll choose."