The Scotland international has missed much of the opening months of the new Premier League season with fitness issues, but has recently returned to action under Gus Poyet.
Although he has not quite yet displayed the form that has seen him heralded as one of the division’s top strikers for some time, Steve Bruce is still keen to lure the ex-Wolves man to Humberside next month.
The Tigers are currently four points clear of the drop zone, and their boss knows that a lack of goals from his current crop of strikers could see them dragged into a fight for safety after an impressive start to life back in the big time.
Fletcher isn’t likely to come cheap, with the Black Cats said to value their forward highly.
But Bruce is ready to test their resolve with a £6m offer, which may tempt Poyet to sell as he plots his own additions.
The Uruguayan currently has Jozy Altidore and Fabio Borini as options in the final third, and could opt to sell Fletcher in order to secure a player to support the duo.