Former Hibernian forward Tam McManus stated on Twitter last month that Fletcher is in Glasgow now and is a very keen on a move to Celtic.
The 33-year-old striker is a free agent at the moment, having left Sheffield Wednesday in the Championship in England this summer.
The former Wolverhampton Wanderers and Sunderland striker scored 13 goals and provided two assists in the league for the Owls this past season, according to WhoScored.
Celtic could do with a striker this summer, as Odsonne Edouard and Leigh Griffiths are their two senior players upfront.
Lennon has been asked about the prospect of Fletcher joining his side this summer.
The Celtic boss told The Glasgow Evening Times about Fletcher: “He is a good player. I am not going to confirm or deny that, I don’t want to talk about individuals.”
Meanwhile, The Glasgow Evening Times has reported that clubs in Belgium, Portugal and the Netherlands international are interested in signing Marian Shved on loan from Celtic in the summer transfer window.
The report has claimed that the Bhoys are considering the options, as they plan to send the Ukrainian winger out on loan for the 2020-21 campaign.