Olsson would cost around £2million.
Allardyce said: "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.
"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."