Cole, who is on loan to Burnley from Sunderland, was arrested on 25 February at his home in Alderley Edge, Cheshire.
The 36-year-old married his long-term girlfriend Shirley Dewar in July 2002.
A police spokeswoman said: "A 36-year-old man from Alderley Edge is due to attend one of our police stations to answer bail."
Cole scored a staggering 68 goals in 84 appearances for Newcastle between 1993 and 1995.
He was signed from Bristol City and took the place by storm with his powerful running, superb finishing, and uncanny partnership with Peter Beardsley.
Left under a cloud when he was sold to Manchester United.