West Ham‘s injury crisis at the left-back position.
The move would reunite Allardyce with Olsson, who played under the current Hammers boss while he was in charge of Blackburn.
The 24-year-old has been at Ewood Park for seven years and established himself as Rovers’ first choice left-back under Allardyce.
The Swedish international has been a first-team fixture this season too, making 21 appearances and Big Sam is keen to sign the £2million rated player to fill the void left by the injured George McCartney and Joey O’Brien.
“If they have made Martin available I would definitely be interested because I worked with the lad at Blackburn when I was there for two years,” Allardyce told The Daily Mail.
“I had a really good time developing him into what I consider to be quite a good player.
“But whether Blackburn are wanting to sell anybody in their plight to get back into the Premier League I don’t know.
“We’ll need to find a left back as quick as we can. Joey O’Brien has a tight hamstring and George McCartney is out for a number of weeks. So our left back area is a little weak at the moment.”
Olsson had looked set to leave Rovers after their Premier League relegation in the summer, after his agent revealed the player would refuse to play in the Championship.
But the versatile defender, who can also play at left-wing, opted to stay put in Lancashire.