The Mail on Sunday claim Rangers want the highly regarded gaffer - who led Brentford to a place in the English Championship play-offs a year after guiding the club to the League One championship - to succeed Stuart McCall this summer.
The talks are not, as yet, official as the Ibrox board anxiously wait to see if the club will return to the Scottish Premiership at the conclusion of the play-offs.
Should Warburton become the next Rangers boss then it’s very likely he’ll bring David Weir with him. The former Rangers captain has been Warburton’s assistant since he took over the reins at Brentford 18 months ago.
Despite almost doing the unthinkable and achieving promotion to the English Premier League with a club whose ground holds less than 13,000 spectators, Warburton has been told his services will no longer be required. The greater London club are overhauling the management structure with a new director of football having recently been unveiled.
Meanwhile, current interim boss Stuart McCall revealed he will sit down with the board in the next few days to discuss plans for next season.
McCall previously expressed his desire to remain at Ibrox beyond the summer and has begun planning for the future despite his future remaining uncertain.