The Hammers, who were in talks with the Sweden international, are thought to have had an opening offer of £2m turned down by Blackburn.
"I think it is based on how desperate they think we are," London24 quotes Allardyce as saying. "Everybody talks about an inflated window and I think that is the case until the last two days. Martin Olsson was of interest to me and I couldn't see anyone else going for him.
"If there were other clubs going for him too I could understand the valuation but there isn't anybody. I'm not saying they won't get that price, they might in the next couple of days, but we went and made our offer and then decided to move into another area."
The former Premier League outfit are thought to be demanding an bid in the region of £4.5m.