The Swans defender was heavily critical of Suarez in an extract from his Premier League diary recounting last season, their first in the Premier League, published this week.
Williams was quoted as saying the Uruguay international was "streets ahead of any player I've truly disliked" and he wanted to "knock him out" for the player's diving antics.
"I have spoken to Ash and Ash has spoken with Luis so there is no issue there," said Rodgers, who along with Joe Allen returns to the club they left in June. "When I saw it I was surprised because in my time there because Ash, knowing his character, is a real good man with good intelligence and maturity and a good footballer player.
"When I saw those comments I spoke to him and got the full explanation of how it has seemingly got out there and he was very quick to want to apologise for that.
"That is done. There is no problem there and I am sure they will shake hands on Sunday and get on with it."