Rangers are keen to replace centre-backs Nasser Djiga and Derek Cornelius, who have returned to their parent clubs after loan spells, and they also need competition at left-back following Jayden Meghoma’s return to Brentford.
Reynolds is being considered as an option at right-back, with Dujon Sterling currently the only player in that position.
The jersey vacated by former captain James Tavernier is up for grabs.
The 24-year-old has been with Westerlo since 2013 and has seven caps for the United States national team.
He had an unsuccessful stint at AS Roma after breaking through at FC Dallas.
Reynolds is not part of the World Cup squad this summer.
Reports in Belgium have indicated that Westerlo are preparing for interest in his services as he enters the final year of his contract.
The Rangers Review revealed last month that Casper Widell, the Excelsior defender, was another name under consideration at Ibrox after being tracked by Rangers over the course of the Eredivisie campaign.
The 23-year-old made 34 league appearances and scored once in the win over Groningen.
Blackburn Rovers and Derby County have also been credited with an interest in Widell in reports in his homeland.
Rangers’ interest in Reynolds comes after Tuur Rommens completed a move from Westerlo to Glasgow in the winter window, making an immediate impression at Ibrox.
Former Light Blues coach Issame Charai is the boss at Het Kuipje and clinched a loan move for Clinton Nsiala in January.
Charai could lose another of his key men to the club where he spent time on the staff under Philippe Clement and Barry Ferguson but Rangers are likely to face competition for his signature.
Rangers have already begun their recruitment drive with the arrival of Lawrence Shankland last month.
The club will be hoping to continue strengthening their squad as they prepare for the new campaign.
