The centre-back’s contract is due to expire in 2022 and his release clause could be around the seven-figure mark.
Souttar, 22, commenced his career with Dundee United, becoming the youngest ever to play in the first-team at 16.
He later joined the Jambos in 2016 and has been a regular for the side, making more than 100 appearances.
The Scottish defender has appeared for 20 games this season and caught the eye with his performances.
He made his international debut last year and has earned three caps till now.
Gerrard looking to strengthen his defence
Steven Gerrard is currently looking to strengthen his side’s back line for next season.
With Joe Worral expected to return to his parent club Nottingham Forrest at the end of the season, the Light Blues are considering Souttar to be his successor at least on an interim basis.
Moreover, the Scotsman can also play as a full-back and as a defensive midfielder, which would be an added advantage for the Gers.
The Light Blues have picked up the momentum with back-to-back wins, recovering from the Old Firm derby defeat.
Gerrard, who is in his first season as the Ibrox manager, wants to end the season on a high note.
Read more Rangers News, click here – Latest Rangers News
The Gers will be facing the Jambos in their next Premiership games and Souttar has the chance to impress against the side, which he possibly could end up in next season.