The Premier League club reportedly had a £2m bid rejected earlier in the week, but have, it seems, returned to the table with an improved offer.
Olsson, who has 14 international caps to his name, is now in a sixth season at Ewood Park, a stay which included Allardyce’s ill-fated tenure.
With first-choice full-backs George McCartney and Joey O’Brien both sidelined, Olsson’s signature would lighten the workload on 18-year-old stand-in Dan Potts.
And while there may still be haggling to be done, Allardyce quashed reports that West Ham have been quoted £7million for the player.
“I don’t think that’s true, but we have made an enquiry. Negotiations are on-going at the moment,” Allardyce revealed.
“If I were strengthening anywhere at the moment, it would be in the left-back position because of our injury problems in that area. So, we’re only looking in that position at the moment.”
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