Rangers are in talks with Robbie Fraser and his representative over a new contract.
The youngster made his debut for the Ibrox club against Dundee in the Scottish Premiership earlier this month.
Philippe Clement then started the left-back on the final day of the league season away at Tynecastle.
Rangers Review states that a two-year deal is the offer on the table for the 21-year-old.
He's out of contract this summer but is set to be handed a chance to stake his claim as part of the first team fold at the club.
In some Rangers transfer news brought to you last week, Jefte has already signed on the dotted line.
It's believed the Brazilian has been drafted in to replace Borna Barisic who is Trabzonspor-bound.
Ridvan Yilmaz is still on the books in the left-back position.
However, with interest in Turkey and Italy during the January transfer window, it seems he could still yet move on to pastures new.
So, Rangers are keen to keep hold of Fraser to keep healthy competition in that area of the squad, as well as Clement making it clear that there needs to be greater usage of the youth ranks at the club.
Ross McCausland became a mainstay under Clement's tenure since his arrival last season.
The likes of Cole McKinnon and Johnly Yfeko have also featured, although not as frequently.
Meanwhile, Jose Cordoba will not complete a transfer switch to Rangers.
The Ibrox club have pulled out of the race to sign Cordoba despite the Panama international being a main target earlier in the summer window.
It's understood Cordoba received a tour of Ibrox and watched the Scottish Premiership fixture against Kilmarnock in a bid to strike a deal.
