The report claims the Championship goal machine is one of Rodgers' top winter window targets. The Liverpool manager wants strength-in-depth behind first-choice duo Luis Suarez and Danny Sturridge.
And Rodgers believes Ings, who has scored 11 goals in 17 league appearances for the Clarets in the Championship this term, could be the perfect back-up option.
Liverpool scouts were monitoring Ings even before the injury to Danny Sturridge, but the news that the England international faces up to two months on the sidelines has firmed up the club's desire to bring in capable replacements.
The England under-21 star would reportedly command a hefty fee, and Burnley will be desperate to hold on to him as they chase Premier League promotion.
They're third in the Championship table, and well placed to mount a title charge in the second half of the campaign.
But the opportunity to cash in on an offer from Liverpool, especially a sizeable one, could be difficult to turn down for a club that often has to sell before it buys.
Burnley sold Charlie Austin to Championship promotion rivals Queens Park Rangers over the summer, but Liverpool target Ings has stepped up in his absence this campaign.