The 31-year-old will run out his contract with Swansea this summer as the Welsh club are reluctant to extend his stay.
The former Blackburn Rovers star couldn’t enjoy enough success with the Swans as he made only 20 appearances this season and went missing since December due to injury.
Prior to his move to the Welsh club, the Swedish international played for Norwich City over four seasons with 129 appearances.
Olsson has earned 48 caps for the Swedish national team, bagging 5 goals.
Should the Light Blues move for Olsson?
The Light Blues managed to cope with the absence of Borna Barisic as their alternate option, Jon Flanagan played well in the latter half of the season.
The former Liverpool full-back has a contract with the Gers until the end of next season, whereas Barisic is expected to start once he gets back into the fold
Given this, Steven Gerrard doesn’t have the necessity to sign Olsson, who is already in his 30s.
Gerrard fared well in his first ever managerial season at Ibrox as he led the Gers to finish second behind Celtic.
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Though he couldn’t grab any silverware, the former Liverpool captain has made a flurry of signings to contend for Premiership glory in the forthcoming season.