Then a Hibernian player, Fletcher has claimed Celtic had a bid for him rejected at the start of 2009.
"I was linked with Celtic in the January window," he said. "They put an offer in for me and it got rejected. And I went and saw the chairman (Rod Petrie) and says like, what’s the script? He openly says to me, listen, I’ll let you go in the summer, but you’re not leaving now. I was like, alright.
"Obviously I was still a bit like, can you not just let me go? I tried to push it a little bit - you’ve obviously got to try your luck. And he was like, listen, you’re not going. So I was like, alright."
Instead, Fletcher has claimed he was told that Hibernian's preference was for him to continue his career in England's Premier League, which is what ultimately happened with Burnley.
But asked whether he was desperate to play for his boyhood heroes, Celtic, the 32-year-old replied: "I did want to go, aye.
"Because they had a good squad at the time. Strachan was the manager. He brought it up to me when he was the Scotland manager!"
Fletcher went on to forge a successful career south of the border, joining Wolverhampton Wanderers and Sunderland for substantial transfer fees before moving on to Sheffield Wednesday at the end of his Mackems contract.
The 33-cap Scotland international has just ended his third season at Hillsborough as top scorer and still has another year to run on his deal.
Meanwhile, one of Fletcher's former strike partners, Gary Hooper, has been linked with a return to Celtic after his release by Sheffield Wednesday.
Would the Sheffield Wednesday striker have been a good addition for Celtic?
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