The Hammers are believed to have tabled a £2m bid for the Swedish international last week, as manager Sam Allardyce looks to strengthen his defence.
However, this approach was rebuffed by the Championship club, who value the defender highly.
It is said that they are holding out for around £6m, a figure that the Londoners are unwilling to match.
Allardyce is happy to increase his bid, but it remains unclear as to whether the new sum will meet Blackburn’s demands.
Olsson has reportedly asked the club to allow him to leave, as he is keen to return to the Premier League and work under Allardyce once again.
The player’s demands may force the Ewood Park-based side’s hand, although they are keen to keep their squad strong in a bid to gain promotion to the top-flight.
West Ham are currently without first-choice left-back George McCartney, who is sidelined through injury.
They have been linked with Aston Villa outcast Stephen Warnock recently, but is said that Olsson is their top target.
Allardyce is hopeful that a deal can be done, after claiming that injuries have exposed the lack of defensive options he has at his disposal.