With the Premier League season due back next weekend, the Irons are in the market for a left-sided defender after injured Aaron Cresswell was ruled out for four months.
The Mail reported on Wednesday that West Ham had turned their attention to Inter Milan's Davide Santon after walking away from the Olsson negotiations.
Norwich knocked back a £3 million bid by the Hammers, according to The Sun, but McBride feels that West Ham boss Slaven Bilic should return with a bigger and better offer rather than settle for the former Newcastle defender.
"I think they need to up their bid for Olsson," McBride told ESPN. "I really like Olsson - not only as an attacking option going forward, but defensively he's very strong."
The 28-year-old indeed is a very capable left-back, but West Ham don't want to pay over the odds for what is essentially going to be a stop-gap until Cresswell recovers.
That being said, Bilic also needs to strike a balance between cheap and competent. Four months is a long time in football and the Irons' season will undoubtedly suffer if Bilic does not get the replacement spot on.
They kick off the Premier League season away to Chelsea on August 15.