The Reds are keen on the young England international who is hoping to be part of Roy Hodgson’s squad for the World Cup this summer despite heavy competition.
Shaw is still only 18 years old but has cemented his place in the Saints side this season and is now the target of Chelsea, Arsenal and Liverpool.
Rodgers wants to make this summer his most successful transfer window with the added incentive and money arriving for qualification to the Champions League and maybe even a Premier League title.
The defence is the only issue at Anfield with Glen Johnson currently filling in at left back, and so Shaw is seen as the perfect addition to Rodgers’ squad.
Southampton do not want to sell another academy product and will play hard ball over a price, leaving Liverpool to find the big money for the purchase.