A user, believed to be a man from the Derbyshire area, referred to Chelsea star Cole as a "choc ice" on the site
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.
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The incident comes after Chelsea captain Terry was cleared of a racially aggravated public order offence at Westminster Magistrates’ Court last week.
The “choc ice” term is understood to mean “black on the outside, white on the inside.”