After scoring 38 goals during a four-year period at Hillsborough, the 33-year-old is now a free agent.
While the veteran has been linked with a number of clubs, it appears that Celtic are the frontrunners for the Scotland international's signature.
Manager Neil Lennon has told Sky Sports News that discussions have been held with the player's representatives.
Fletcher has not plied his trade North of the border since 2009, with his form at Hibernian earning him a £3m switch to Burnley.
Celtic are also said to be contemplating an offer for ex-Charlton Athletic attacker Lyle Taylor. body check tags ::