The New York Daily News reports the couple claimed Galliano shouted, "Dirty Jewish face, you should be dead", and, "F**king Asian b**tard, I will kill you".
The 50 year old, head designer for Christian Dior, was taken to a police station for a sobriety test and subsequently released without charge.
But Galliano's lawyer, Stephane Zerbib, has blasted the couple's accusations - he alleges it was the fashion guru who was the victim and he's preparing to sue the pair for defamation.
Zerbib says, "There was an argument. Mr. Galliano was verbally attacked but at no time did he use... insults of a racist or anti-Semitic character. We have witnesses to back up his version of events."
The legal representative is now planning to take the couple to court to clear Galliano's name.
Following his arrest, bosses at Christian Dior suspended Galliano pending the outcome of a police investigation into the incident.