"Peter Odemwingie is an important player for us and a player we believe in and a player we want to keep and a player who is not for sale," said Hodgson. "We don't welcome offers for Peter Odemwingie. He is a West Brom player at the moment and will be next season.
"We want to keep him and he is under contract. Very simple really. It is very irritating when people just out of the blue suddenly start linking us with other players.
"I presume the link with Andy Johnson is based on the fact we worked together at Fulham and it is a player I admire as a footballer. He did a great job for me but, to be fair, he is not a player we've actually discussed in terms of next season."
The 30-year-old, who has been plagued with injury woes this season, has been with the Baggies since 2010.