A user of the social networking website made the derogatory suggestion - which implied that Cole is 'white on the inside' - whilst tweeting the Peckham-born centre-back on Saturday.
And Ferdinand's reply appeared to back those sentiments, saying: "I hear you fella! Choc ice is classic hahahahahahha!!" The tweet has since been deleted.
"What I said yesterday is not a racist term. Its [sic] a type of slang/term used by many for someone who is being fake," the United man tweeted on Sunday morning in response. "So there."
The comments had caused a storm just a day after Chelsea captain John Terry was acquitted of a racially aggravated public order offence for an incident involving 33-year-old Ferdinand's brother, Anton - a trial in which Cole appeared as a witness to defend his team-mate.
The left-back quickly released a statement following the initial tweet which insisted that his and Ferdinand's friendship would remain unaffected by the controversy.
"Ashley Cole wishes to make it clear that he and Rio Ferdinand are good friends and [he] has no intention of making any sort of complaint," it read.
"Ashley appreciates that Tweeting is so quick it often results in offhand and stray comments."