English Championship side Stoke City also want the 33-year-old and have offered him a two-year deal worth £18,000-a-week, but he is ready to turn it down as he is keen on joining Celtic.
However, Fletcher wants the Scottish Premiership giants to increase their offer and hand him a two-year contract.
The veteran striker was close to sealing a Parkhead move back in 2009, and wants to finally fulfil his dream of playing for them, but they are only ready to hand him a 12-month deal and lesser wages than Stoke.
Hoops boss Neil Lennon wants striking reinforcements this summer, and Fletcher would be a quality addition after bagging 13 goals in 27 league games for Wednesday last term.
The Scotland international has Premiership experience having spent his formative years at Hibernian, and he shouldn’t have a problem hitting the ground running if he moves to Celtic.
The Parkhead outfit have Odsonne Edouard as their first-choice striker, but they need quality options on the bench if they are to beat Rangers to the title and land 10-in-a-row, and Fletcher will be keen to be part of the history-making mission.