The Baggies chief has spoken out on the future of the Nigerian forward, who endured a difficult start to the campaign as injuries and a loss of form hindered his efforts to emulate his first season in the Premier League when he scored 15 goals to ensure the Baggies avoided relegation.
However, Odemwingie, who agreed a new contract at the Hawthorns last summer, has since rediscovered his Midas touch in front of goal with a hat-trick against Wolves and a brace in the recent 4-0 win against Sunderland respectively.
As a result, there has been more speculation linking the former Lokomotiv Moscow hitman with a move away from Albion at the end of the season with Arsenal the latest club said to be pondering a bid.
And, while Hodgson is hopeful that Odemwingie does stay at Albion in the long-term future, he accepts that a bid which is too good for all parties concerned could come in.
He told The Sun: "If we get one of those offers you can't refuse, I'd be delighted to say, 'Peter, you've shown what a great player you are - we can't compete with this'.
"If one of the big four sides comes in, you can't compete."
But, Hodgson added: "You can earn huge money in Saudi Arabia or China, with no tax, but, no disrespect, these are not top leagues."