A user, believed to be a man from the Derbyshire area, referred to Chelsea star Cole as a "choc ice" on the site and Manchester United defender Rio Ferdinand then replied: "I hear you fella! Choc ice is classic hahahahahaha!!".
Derbyshire Police said it was now investigating the original Tweet after receiving complaints from members of the public.
The incident comes after Chelsea captain Terry was cleared of a racially aggravated public order offence at Westminster Magistrates' Court last week. It was alleged Terry had maliciously called Rio's brother Anton a "f****** black c***" during a game last October.
Cole, 31, had told the trial that Terry, his Stamford Bridge captain, was not racist.
The "choc ice" term is understood to mean "black on the outside, white on the inside".
A spokeswoman for Derbyshire Constabulary said: "We have received complaints from members of the public regarding alleged racist comments made on a social networking site. These concerns will be fully investigated to establish whether any criminal offences have been committed."
Cole moved to calm the situation at the weekend after users began discussing the comments and reacting to them.
In a statement issued through his lawyers, the footballer said: "Ashley Cole has been made aware of the discussion following comments appearing on Twitter and wishes to make it clear that he and Rio Ferdinand are good friends and Ashley has no intention of making any sort of complaint. Ashley appreciates that Tweeting is so quick it often results in off-hand and stray comments."
Ferdinand later tweeted: "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." A spokeswoman for Greater Manchester Police said the force was not investigating the comments made by Ferdinand.
Source: PA
Source: PA