Former Sunderland striker Fletcher is a free agent at the moment, having left Sheffield Wednesday in the Championship this summer.
The report has claimed that initial talks between Celtic and the 33-year-old striker have taken place, with manager Neil Lennon an admirer of the player.
However, according to the report, Fletcher has received long-term offers from clubs at the top end of the Championship in England, and Lennon is in no rush to match them, although he is keen on bringing in a new striker this summer.
According to WhoScored, Fletcher made 23 starts and four substitute appearances in the Championship for Wednesday this past season, scoring 13 goals and providing two assists in the process.
The former Sunderland striker made 32 starts and eight substitute appearances in the league for the Owls during the 2018-19 campaign, scoring 11 goals and providing two assists in the process, according to WhoScored.
Good signing for Celtic?
Odsonne Edouard and Leigh Griffiths are the two main strikers at Celtic at the moment, and the Glasgow giants could do with another player upfront.
However, Fletcher – described by Wednesday manager Garry Monk as “fantastic” in The Star in December 2019 – is 33 years of age, and the Glasgow giants have to think carefully before handing him more than a one-year contract.