The Blackburn Rovers' Sweden international is a target for the Premier League club, who have been hampered by an injury crisis at left-back this season
The 24-year-old was part of Sweden's Euro 2012 squad last summer and has been linked with a £7 million move to Upton Park during the January transfer window.
Allardyce has confirmed West Ham are negotiating with Blackburn over Olsson but insists the fee reported is not accurate.
On West Ham's reported bid for the full-back, Allardyce replied: "I don't think that's true, no, but we have made an enquiry.
"I think that if I was strengthening anywhere at the moment it would be in the left-back position because of our injury problems in that area at the moment. We are only looking at that position at the minute.
"If there's a player there that we think can improve the squad we'll try to move on him."