The Yorkshire Evening Post understands that Diagouraga and his representatives are currently at Elland Road to discuss terms over a permanent move to West Yorkshire.
Rangers are also interested in singing the 28-year-old midfielder, but the Whites seem to have stolen a march on the Scottish side.
Diagouraga has made 25 appearances in the Championship for Brentford this season, having established himself as a key player for the Griffin Park side.
He has been with the Bees since 2009, having joined them on loan from Peterborough before making a permanent switch in the summer of 2010.
Diagouraga began his career with Watford and was named the Brentford Supporters’ Player of the Year last season.