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'.
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.
"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."
