Cole, who gave evidence at team mate John Terry's racism trial last week, was labeled 'choc-ice' by a Twitter user thought to live in Britain.
The user posted a message to 33-year-old Ferdinand shortly after Terry had been cleared of a racially aggravated public order offence at Westminster Magistrates' Court last week.
Former England captain Terry was accused of abusing Ferdinand's younger brother Anton during a Premier League match between Chelsea and QPR.
"Looks like Ashley Cole's going to be their choc ice," said a tweet directed to Ferdinand.
"Then again he's always been a sell out. Shame on him."
Ferdinand replied with: "I hear you fella! Choc ice is classic! hahahahahahha!!"
The term 'choc-ice' is understood to have racial connotations meaning a person is 'black on the outside' and 'white on the inside'.
Ferdinand deleted the post but it was captured by Twitter users who spread it across the social networking site.
He defended his actions claiming the tweets were 'slang' for someone who is acting 'fake'.
"What I said yesterday is not a racist term. It's a type of slang/term used by many for someone who is being fake. So there," he posted.
Complaints have since been filed by the public to Derbyshire Constabulary who issued a statement confirming they were investigating alleged racist comments directed at Cole.
"Derbyshire Constabulary has received complaints from members of the public regarding alleged racist comments made on a social networking site," a statement said on Tuesday.
"These concerns will be fully investigated to establish whether any criminal offences have been committed."
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