The Japan international arrived at Celtic Park from J-League side Vissel Kobe in the summer and has hit the ground running at his new club.
Furuhashi has quickly become a fan favourite at Celtic, with each one of his 16 goals across all competitions so far this season raising his stock.
Former Hoops boss Barnes has hailed Furuhashi as a brilliant addition to Celtic and stressed he needs to keep providing the goods up front for the remainder of the season to help them try to knock Rangers off their perch in the Scottish Premiership.
However, Barnes insists that even if he ends up having a great first season in Scotland that does not guarantee Premier League clubs will be interested in taking him south of the border next summer.
“Kyogo Furuhashi has been brilliant for Celtic so far this season”, former Bhoys boss Barnes told Bonus Code Bets.
“He is someone who has a great attitude to play football and wants to get his head down and perform each week.
“However, even though he might have one good season in Scotland with Celtic, doesn’t mean he’ll get any interest from Premier League clubs.
“The most important thing for him at this moment in time, is to stay at Celtic, continue working hard and help Celtic challenge Rangers for the Scottish Premiership title as best as he can.”
Celtic saw striker Odsonne Edouard leave the club for Premier League side Crystal Palace in the summer and fans will be hoping Furuhashi will remain at the club in upcoming seasons.