South Korea international Ki signed for Newcastle on a two-year deal in June 2018 after his contract at Swansea City expired and he was a regular squad member during his debut season, making 18 Premier League appearances under then-manager Rafael Benitez.
However, the 30-year-old has struggled for playing time since Steve Bruce's arrival in the summer and the midfielder has made just one league start, leading to reports he is looking to leave St James' Park in the January transfer window.
The English quartet of Isaac Hayden, Jonjo Shelvey and the Longstaff brothers, Sean and Matty, have both moved ahead of Ki in the pecking order and an exit appears to be on the cards.
It is being claimed Celtic boss Lennon, who worked with the Gwangju-born star during his first managerial stint at Parkhead, is looking to be reunited with his former player in the new year.
Ki has just over six months left on his current deal and it is thought a cut-price deal could be agreed between both parties, while a loan until the end of the campaign may also suit if the Bhoys pay all of his wages.
A temporary move would then allow the midfielder to join Celtic on a free in the summer if he does enough to impress Lennon, who is eager to add fresh faces to his squad as they challenge for honours on both the domestic and European stage.