The Uruguayan international has been accused of racially abusing Evra during Saturday's 1-1 draw at Anfield but he has pledged is innocence whilst Evra has been asked to provide proof via a witness who may have heard the apparent remarks.
"The only thing I will say - and then it is put to bed - is that the football club and everyone at the football club is totally and utterly fully behind Luis Suarez," said Dalglish.
"There was an allegation after the game about him diving all over the place and there was an allegation from Patrice Evra.
"Obviously the two things are emotive but we support the wee man on both things.
"At the start of the week the club made their position known and apart from what I have said we won't be adding to it.
"We are fully looking forward to a complete, transparent report from the FA and we will co-operate 100%."