The Daily Star Sunday says Hodgson wants Jeremy Peace to use West Brom's £18m profits to keep defender Olsson.
Albion chairman Roy Peace has just produced annual accounts which have recorded a staggering £18.9m pre-tax profit.
And boss Roy Hodgson said: "Jonas will be entering the last year of his contract soon and no club really wants that to happen with the players they are anxious to keep. Albion are anxious to keep Jonas.
"Talks are ongoing. We are not panicking he will walk out of the door in May, but the sooner the talks reach a conclusion, the better for everyone."