Souttar remained on the bench during their Championship clash with Coventry City over the weekend.
The 24-year-old was also absent from Leicester City’s 20-man squad that defeated Burton Albion in the League Cup tonight.
However, Rangers aren’t the only club pursuing the Australian international.
The move could see a familial reunion, as Souttar’s older brother John is already a part of the Rangers squad, having joined their ranks last year.
Amidst a flurry of on-field action for the Ibrox outfit this week, they must wrap up their transfer dealings.
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Rangers have made nine signings this summer, picking up Cyriel Dessers, Danilo, Sam Lammers, Dujon Sterling, Leon Balogun, Abdallah Sima, Jack Butland, Kieran Dowell and Jose Cifuentes.
They could add Souttar to that list as he looks set to leave the King Power Stadium this summer despite signing a long-term contract with Leicester City in January for £20 million.
The Aberdeen-born centre-back is a dedicated Rangers fan. He has Scottish Premiership experience after playing for Dundee United and Ross County.
Rangers have had a topsy-turvy start to their 2023/24 football season, losing their opening league game to Kilmarnock before defeating Servette 2-1 in their Champions League qualifier.
They face Livingston in the league this weekend and will hope to make up ground on Celtic, who won their opening game against Ross County.
Celtic are led by Brendan Rodgers, who bought Souttar at Leicester and reportedly looked his way this summer.
However, Rangers are targeting the defender and want to make a concrete move.
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