Parkhead boss Neil Lennon was asked about the possible arrival of the ex-Hibs striker following the club’s 2-0 win over Ross County in Sunday’s friendly.
Fletcher is out of contract following the expiry of his contract with Sheffield Wednesday.
Lennon said: “He’s on a long list of players that I am sure a lot of clubs are looking at.”
Having re-signed Mohamed Elyounoussi, Celtic have set their sights on bringing in a goalkeeper and a striker.
According to reports in Greece, the club have made a second offer for goalkeeper Vasilios Barkas.
With little progress in trying to persuade Fraser Forster to return for a third spell the AEK Athens goalkeeper is at the top of the list to come in and compete with Scott Bain for the No.1 position.
With regards to a striker, Celtic have been linked with a number of players, including Peterborugh United’s Ivan Toney and Albian Ajeti from West Ham.
Fletcher, however, would be a cheaper alternative. The 33-year-old hit 13 goals for Sheffield Wednesday last season.
Since leaving Hibs for Burnley in 2009, the forward has played for Wolves, Marseille and Sunderland.
Lennon is hopeful of adding to his squad in the coming days.
He said: “We will probably have more on a few things over the next few days.
“I am happy with the squad but we can improve it and that’s what we are looking to do.
“It is a difficult environment as we aren’t sure how the pandemic will impact on the market. But we do want to bring players in and I don’t think we’re a million miles away.”