Liverpool boss Rodgers sees Swansea's Williams as No1 Carragher replacement
Securing the services of a dominant centre-back is the club's overriding priority in the next transfer window and Williams tops their shortlist, says the Liverpool Echo.
Rodgers worked with the 28-year-old during his two years in charge of the Swans and believes he has all the qualities required to succeed at Anfield.
The Wales international skipper, who only penned a new deal back in October, is under contract until 2015 and would command a fee of around £8million. He has also attracted interest from Arsenal.