Brendan Rodgers has already completed the signing of relegated striker Danny Ings and is now considering a move for the England hit man despite his hefty £15m price tag.
Austin notched an impressive 18 goals for Rangers last term in their unsuccessful battle against the drop.
Incoming Newcastle boss has also placed Austin on his wanted list, but it now appears he may face some stiff competition.
As well as Newcastle, it has been reported that Jose Mourinho is also an admirer of the striker and he is also interested in bringing him to Stamford Bridge to add options to his depleting strike force.
It is reported that although Rodgers is interested in the 25 year old, he is not their first choice summer target and that he may look elsewhere before Austin.
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