The Reds have been heavily linked with the Welsh international in recent months, as they look to find a replacement for the retiring Jamie Carragher.
Rodgers coached Williams during his time in charge of the Swans, with the centre-back a key part of his squad that secured promotion and maintained Premier League status.
With Martin Skrtel also the subject of speculation regarding a switch to Russia, the defensive leader is top if the club’s wish list.
Rush believes that Williams, who captained Wales against Croatia on Tuesday, would be an ideal fit at Anfield:
“To get in Ashley Williams would be great,” he told the Liverpool Echo.
“I’ve seen him play for Wales on a number of occasions and he is organised and a good captain.
“He knows what he is doing and the link to Liverpool is natural because Brendan Rodgers managed him at Swansea.
“At the right price Swansea would let him go although that they are in Europe next season may have a bearing on his decision.
“But he would be good for Liverpool with his experience.”
Rush, who scored 346 goals for Liverpool, also feels that the club should be looking for natural leaders to replace Carragher and eventually Steven Gerrard:
“We need to replace not just what Jamie brings on the field but off it as well.
“Every teams needs people like Carragher.”
Williams is regarded as a key man at Swansea, but it is thought that an attractive bid may tempt them to sell up this summer.
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