The Swans defender was heavily critical of Suarez in an extract from his Premier League diary, published this week, which recounts last season, Swansea's first in the Premier League.
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.
Rodgers was taken aback when he read those comments and has spoken to Williams, who in turn has talked to Suarez, in an attempt to prevent the situation escalating ahead of tomorrow's match at the Liberty Stadium.
"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 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."
The fact Rodgers was able to use his good relationship with his former club to intervene in the matter has no doubt helped minimise lingering ill-feeling.
Even so, Swansea boss Michael Laudrup admits he does not know if Williams and Luis Suarez will shake hands.
Laudrup would not offer his opinion on Williams' comments about Suarez, but believes the former Ajax man divides opinion because of the number of incidents he is caught up in. Laudrup said: "I will keep my opinion about Suarez to myself. I don't want to say I'm for or against him, or that he's a diver. I know he's a great player."