Mark Warburton’s side have already had a bid rejected for Diagouraga, but they could make a repeat bid for the defensive midfielder in the near future.
Diagouraga has just 18 months left on his contract at Brentford, and is said to be unhappy with his current situation at the Championship club.
As a result, he is keen to speak to Rangers - with a move appealing to the former Peterborough United man.
Warburton has targeted Football League players ever since moving to Ibrox, and he has already completed a deal to sign Accrington Stanley duo Josh Windass and Matt Crooks in January.
It seems that Diagouraga is the next man on his wishlist, as the Light Blues look to bolster their midfield options.
Warburton knows Diagouraga well, as the pair linked up together during the 53-year-old boss’s time at Griffin Park.
Brentford are keen to keep hold of the 28-year-old, who plays a key role for them in the heart of their midfield, but his future is very much up in the air at the moment.