Extracts from the Swans' player's new book, 'My Premier League Diary', revealed that he "wanted to knock [Suarez] out" and told how the defender feels that the Uruguayan shows "utter contempt" for fellow footballers.
The Welshman also accused the former Ajax attacker of diving on a number of occasions during their clash at Anfield last season, as well as having an arrogance that suggests that he thinks he is "untouchable".
Despite the 28-year-old's strong words, the Reds' coach, who was in charge of the Welsh side when Williams wrote the book, played down talk of a rift between the pair and expects that they will shake hands when the sides meet at the Liberty Stadium.
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"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."
The two teams go into the Premier League fixture with just one point separating them - the Swans sitting in 10th place with the Merseyside outfit trailing in 11th.