Reports in the last seven days have linked the former Hibernian, Burnley and Wolves striker, bought by Sunderland for a sum in the region of £12m some 18 months ago, with a cut-price move to Celtic during this transfer window.
While sources at the Parkhead club are privately increasingly gloomy about the prospect of such a deal going through, it is true that the Scotland internationalist's career stands at a crossroads right now.
Fletcher, who turns 27 in March, has been in and out of the first team since Gus Poyet replaced Paolo Di Canio as the occupant of the manager's office at the Stadium of Light, although it was a positive sign that he was included in the starting line-up for Sunderland's Capital One Cup semi-final first leg against Manchester United last night.
While it was also heartening for the player to hear the Uruguayan speaking in the lead-up to the game about his desire to keep him, in the next breath he also admitted that no player at the club, currently rock bottom of the Barclays Premier League, is unsaleable. Rather than shipping players out to embrace the inevitable this summer, Poyet wants to bring in three or four bodies in a bid to escape relegation, with Fletcher's fellow Scotland internationalist Liam Bridcutt and winger Will Buckley about to join from Poyet's former club, Brighton.
Fletcher, the scorer of just three goals in 18 appearances this season, is rated the best finisher at the club and has worked hard on his strength and heading, but it is thought a fee rising to £10m could allow the club to reinvest in a forward more suited to playing the lone striker's role in Poyet's favoured formation. As long as that was the case, Sunderland's fans would reluctantly wave him goodbye.
"Of course I don't want to sell Fletcher," said Poyet, who insisted the club had received no offers for the player. "He's our top scorer and he's the one who is going to score the goals and make the difference. If players don't play, sometimes it can be a tactical reason and sometimes we don't explain it because if you did that every time you would not stop calling players. But I'm not the type of person to say 'no-one is for sale' and then we sell one. Why? Because every single player has a price."
If it comes down to hard cash, Celtic undoubtedly are up against it. With the player having two-and-a-half years remaining on a contract which guarantees him around £50,000-a-week, the Parkhead club would require to find funds for a record transfer fee, break their existing wage structure and hope the player is prepared to take a sizeable wage cut. On the face of it, there are probably too many obstacles to be overcome.
But his other potential destinations are not exactly trouble-free either. Moving to Hull City, who reportedly had an £8m bid for the player rebuffed on Monday evening, is every bit as likely to result in relegation, a feeling of which the player has already had too much experience.
Then there is Newcastle, Sunderland's north-east rivals, who would offer a decidedly fraught change of allegiances.
"While he is quite a well respected player around the Premier League, every team he has played for has got relegated," said Sunderland fanzine editor Martin McFadden. "Maybe he thinks he could go back to Scotland and actually win some stuff."
While it might not be to the ultimate benefit of his bank balance, a move to Parkhead would certainly tug at the heart strings. He would rejoin John Park, the club's director of football development, the man who set his career on its current course. Fletcher, a child of the armed forces, born in Germany, ended up staying on with his uncle in Hamilton after the untimely death of his father Kenny to cancer.
"John is from Hamilton as well, and he saw me playing for the boys' club and asked to come in for a trial," Fletcher has said in the past. "He has been like my coach all the way through the ranks, always looking out for me as a Hamilton boy."
Taking centre stage for Celtic in the SPFL and the Champions League would certainly be a risk-free environment to play out the best years of his career. He would also be safely under the watchful eye of Gordon Strachan with Scotland.
Not so long ago his international future was uncertain. Right now it is the surest thing he has going.