The Anfield manager has been tracking the Championship star for much of the season, and the report claims Liverpool are one of four Premier League clubs keen to snap him up before the end of the month.
Newcastle, Stoke and Aston Villa are also watching the 21-year-old forward, with the Premier League clubs aware that Burnley could be forced to cash in should a significant offer come in.
The Lancastrian club sold Charlie Austin to Queens Park Rangers for £4m over the summer. Ings immediately stepped in to replace the departed Austin, and he's bagged an impressive total of 18 goals so far this term.
That haul has attracted interest from Premier League clubs - like Liverpool and Newcastle - who are looking to add a forward in the January transfer window.
Liverpool have impressively negotiated their Premier League fixtures without Daniel Sturridge - he's been missing through injury - but Rodgers is still keen to add further strength in depth.
The Reds have enjoyed a strong first half of the season, and the Liverpool boss wants to build upon that foundation to push towards a Champions League qualification spot.
And Ings, who the report claims could be available for between £5m-8m, could be part of making that happen.