The Jamaica international will leave Leeds when his current contract with the Whites runs out in the summer.
It has now been claimed by The Lancashire Telegraph that Blackburn are interested in the 29-year-old midfielder as well, and that they want to sign him on a free transfer in the summer.
According to the report, Rovers manager Gary Bowyer is “hampered by the embargo that has been placed on the club for failing Financial Fair Play”, but he is “determined to add more experience and strength” to his midfield.
Austin joined Leeds from Norwegian side SK Brann in 2012 and went on to make 112 appearances for the West Yorkshire outfit, scoring 10 goals in the process.
The 29-year-old played 30 Championship matches for Leeds this season, scoring three goals and creating 23 chances in the process.
Austin had a pass accuracy of 79% and a shot accuracy of 38%, and he won 37 headers, 17 dribbles and 62 tackles.