The winger has been linked with the Elland Road side on a consistent basis.
Marcelo Bielsa, when Leeds boss, was understood to rate the former Liverpool youngster, while that interest has been retained under Jesse Marsch.
According to the Daily Mail, Leeds are considering making a move in the final days of the window.
Kent was signed by Rangers under Steven Gerrard for £7million after a successful loan spell from the Anfield giants.
It was around that time Leeds showed an interest and would eventually have a £10million bid rejected by Rangers in 2020.
Any move is likely to depend on the future of Dan James who is wanted by Tottenham Hotspur who are looking to add a winger before they allow Bryan Gil to depart.
Kent has been a key player under Giovanni van Bronckhorst and provided two assists in the weekend win over Ross County.
He has been challenged by his manager to score more goals after netting just three last season.
“If you see his stats last year one of the things we wanted was him to keep assisting the players but also score goals,” Van Bronckhorst said.
“I think for him he always has the full-back behind him who’s coming a lot.
“Borna (Barisic) is always supporting and being right-footed your first intention is to go inside and that makes it really hard for defenders.
“He’s playing well, with the second Colak goal he started the move with the turn and pass to Colak.”