Cole was released by Sunderland and is reported to have rejected a contract offer from Burnley.
Clarets boss Owen Coyle had offered Cole, who was on loan at Burnley last season, a pay-as you-play-deal.
The Daily Mail says that this deal has failed to tempt Cole and the former England international is seriously considering retirement.
1993/95 A.A.Cole 83/1 68
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 and said he was joining a better club. OK, perhaps he was, but we didn't want to hear it. Born in Nottingham.