Andy Halliday and Jon Flanagan have both featured in the position, but manager Steven Gerrard is keen on a primary left-back after Borna Barisic failed to impress.
Olsson left English Championship outfit Swansea last month after his contract expired, and the free agent is currently considering his options as he finds a new club.
Rangers already have a suitor to contest with for the signature of the 31-year-old in Nottingham Forest, but beating competition and landing the Swede will be huge for Gerrard’s side.
After watching bitter rivals Celtic win the domestic treble for the third season in a row, the Light Blues are looking to strengthen their squad this summer in order to challenge better next season, and adding the experienced Olsson to their ranks makes sense.
With 48 caps for his country and almost 200 Premier League appearances under his belt, the former Norwich City star brings a lot to the table.
That he is available for free makes him a bargain of a signing if Rangers snap him up, and after missing the majority of last season to a ruptured Achilles, Olsson will be looking forward to impressing wherever he finds himself in 2019-20.