Cole failed to score in 11 games for Forest after joining the club in July and his contract was cancelled by mutual consent after only three months.
The 37-year-old will now look to pursue a career in coaching or management.
"I've all this experience and I don't want to keep it to myself," said Cole.
"I want to give something back, I don't think this is the end of the Andrew Cole story. Hopefully it's a new chapter."
Cole started his career at Arsenal but only made one appearance before moving to Bristol City in 1992, and it was there he made his name, scoring 20 times in 41 league appearances.
His performances at Bristol secured him a £1.75m move to Newcastle United in 1993 where he became a fans favourite and established himself as one of the best strikers in English football.
Newcastle manager Kevin Keegan controversially sold Cole to Manchester United after just two-and-a-half seasons at St James' Park and it was at Old Trafford where he enjoyed the most successful period of his career.
I want to give something back, I don't think this is the end of the Andrew Cole story
Scoring 93 league goals for the Red Devils, his partnership with Dwight Yorke was a key factor in United's treble-winning season in 1998-99. He also won four other Premier League titles and an FA Cup winners' medal in 1996.
But despite his success at club level, Cole struggled to establish himself in the England team, scoring just once in 15 appearances.
After leaving United in 2001, Cole went on to play for Blackburn, Fulham, Manchester City, Portsmouth, Birmingham, Sunderland and Burnley before joining his hometown club Nottingham Forest in July, 2008.
But after finding his first-team appearances limited, Cole decided to call time on his 19-year playing career.
Cole's Premier League scoring record of 187 goals is bettered only by Alan Shearer, who has 260.
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