The Citizens are bidding to bring in a replacement for Julian Alvarez, who has made the move to Atletico Madrid, and a new forward is expected to arrive before the deadline.
According to The Athletic, Furuhashi is on Man City's radar, with the Premier League champions giving serious consideration to making a move for the 29-year-old, who has been with Celtic since July 2021.
The Japan international has scored 73 goals and registered 16 assists in 135 appearances for his Scottish outfit in all competitions, including 42 goals and 10 assists in 81 Scottish Premiership outings.
Furuhashi has another three years left to run on his contract with Brendan Rodgers' side, but it is being reported that he is on a two-man shortlist with another young forward.
Man City 'weighing up' move for Furuhashi
Transfer expert Fabrizio Romano has claimed that Man City had 'initial talks' with Celtic earlier this week, and a new attacker will become a priority for the Citizens once Ilkay Gundogan's return has been secured.
Gundogan is set to leave Barcelona in the closing stages of the transfer window to return to Man City, with head coach Pep Guardiola said to be key to the move.
The 33-year-old has allegedly received lucrative approaches from Qatar, but he is preparing to return to the club that he represented between 2016 and 2023.
Gundogan was a vital player for Barcelona last season, scoring five times and registering 14 assists in 51 appearances in all competitions, but the Catalan outfit want to remove his salary from their budget, and an announcement over his move back to the Etihad Stadium is thought to be imminent.
Would Furuhashi be a good signing for Man City?
Furuhashi would not arrive at Man City as a guaranteed starter, with the forward instead expected to play a rotational role, with the Citizens in line for another busy campaign.
His ability to operate in a number of different forward positions would be a huge boost, and the Japan international has already helped Celtic win both of their league matches this season, providing an assist in the team's 4-0 success over Kilmarnock earlier this month.
It is obvious that Man City need to bring in a replacement for Alvarez, especially with Oscar Bobb recently undergoing surgery on a broken leg.
Jack Grealish failed to make his mark last season, and while Savinho was impressive in his debut against Chelsea last weekend, there are some concerns over a long-running knee problem.
Much will depend on price, as Man City would not be willing to pay a significant fee for Furuhashi, and Celtic are in a good position to hold firm due to the length of time left on his contract.