The Gers chief of staff, Graeme Murty, has already prepared an £850,000 bid for the 24-year-old defender according to the Daily Mirror.
Brendan Rodgers, on the other hand, has already brought Marvin Compper from RB Leipzig at the beginning of the transfer window, but Erik Sviatchenko left the Hooks to join Midtjylland soon after that.
Jozo Simunovic is on his way out, which may open the door for another defender to arrive in Parkhead, and Barbet might be the right option for the former Liverpool manager.
Barbet has had a terrific first half of the season in the Championship, proving to be one of the most reliable defenders in the league.
However, this is just a speculation for the moment, as Rodgers seems oriented toward Serbian defenders Dusko Tosic who is currently playing for Besiktas, and Neven Subotic, who stands on the exit door of Signal Iduna Park.
