The 23-year-old has already netted a mightily impressive 20 goals in all competitions for the Clarets this season, prompting admiring glances from a host of top-flight sides.
Reds boss Brendan Rodgers is known to be in the market for a new forward when the transfer window reopens, as he looks to add more attacking options to his Anfield ranks, that currently boasts Luis Suarez as the only fit, and recognised first-team striker.
Detractors of the former Swindon star suggest he may not have the technique to make it in the Premier League, but his finishing ability is in great demand, and Burnley would be susceptible to offers for a player they signed for just £1.5million last year.
Austin has been watched closely over the past five games, with scouts deployed to assess his capability of making the step up. Whether or not he is deemed good enough, though, it should all become clearer in January.