The Sunderland striker is said to fancy a move to Parkhead.
Fletcher in action for Marseille
Fletcher is set to be released by the Mackems, having spent the second half of the campaign on loan to Marseille.
The 29-year-old is said to have a number of options to consider, though a return to his native Scotland is deemed the most likely.
Fletcher is set to leave the Stadium of Light on a free transfer
The Bhoys have been linked to the former Hibernian player on numerous occasions, most recently in January, but Fletcher made a surprise move to France instead.
Fletcher's wage demands are said to have thwarted Celtic's attempts to sign him then, though an anticipated summer clear out - which is set to commence with Colin Kazim-Richards - could leave the Scottish champions better placed this time.
Kazim-Richards is reportedly on his way to Brazil
The Scotland international, whose clubmate Danny Graham is also thought to feature on the Bhoys' list of targets, is rumoured to be tempted by a move north.
England-born Fletcher left Hibs for Burnley in 2009, where his form prompted a big-money move to Wolverhampton Wanderers, who later sold him to Sunderland for a reported £12 million.
Fletcher celebrates scoring for Wolves