The Black Cats striker is out of contract in the summer and is considering his options.
The Scotland forward is out of contract at the end of the season and seems unlikely at this point to be offered an extension to his stay at the Stadium of Light.
He reportedly has several offers on the table at present, with Chinese duo Shanghai SIPG and Guangzhou R&F both having enquired about his availability.
Both of those clubs are currently willing to go above his £3m-a-year-deal with the Black Cats to try and tempt him into a move to the Chinese Super League.
He is set to reject those offers, however, and would instead prefer a move up north to join boyhood club Celtic, report the Mirror.
The Scottish giants are equally interested in the player as he is in them, with Ronny Deila already planning ahead for the summer transfer window.
It is unlikely that they will be able to match the offers from the two Chinese clubs, or his current Black Cats deal, but Celtic are said to have already opened talks with Fletcher's representatives about an incentive-based deal.