Hammers boss Sam Allardyce has highlighted a left-back as one of his main targets in the transfer market after securing deals for Joe Cole, Marouane Chamakh and Wellington Paulista.
Joey O’Brien is currently filling in on the left hand side of the club’s backline, with first-choice full-back George McCartney side-lined through injury.
It had been reported that out-of-favour Aston Villa defender Stephen Warnock was the Upton Park club’s main target, however reports are now emerging that Olsson has been the subject of a bid.
The Swedish international was one of the few shining lights as Rovers suffered relegation from the top flight last term, but elected to stay with the club for the Championship campaign.
However, Allardyce is confident that he can lure the 24-year-old back to the Premier League from Ewood Park with a January bid.
It is unclear as to whether Blackburn will be tempted to cash in on one of their star names and much depends on Olsson’s decision.
He joined the club in 2007 from Hogaborgs in his homeland, hailed as one of the rising stars of Scandinavian football.
As well as making over 100 first-team appearances for Blackburn, he has won 14 senior international caps.