Dorus de Vries joined Celtic when Brendan Rodgers was in charge.
The former Celtic striker made the suggestion while analysing the Glasgow giants’ goalkeepers.
Sutton believes that the Hoops need to sign a new goalkeeper, stating that Craig Gordon is coming to the end of his career, and that Scott Bain needs competition.
The BBC Sport and BT Sport pundit has also claimed that 38-year-old former Wolverhampton Wanderers and Nottingham Forest goalkeeper De Vries should not even be at Celtic.
Sutton wrote in The Daily Record: “Dorus de Vries should have been gone long ago and Craig Gordon is coming to the end of his career.
“Scott Bain has done fine since he was introduced to the line-up on a regular basis but he’s not been in long enough to prove he’s No.1 for the foreseeable future and competition’s a must.”
De Vries joined Celtic in the summer of 2016 after leaving Forest in the Championship in England.
Brendan Rodgers was then in charge of the Hoops, and the former Liverpool manager had worked with the Dutchman at Swansea City.
The 38-year-old was signed to help Celtic play out from the back, but he did not do well between the sticks and soon lost his place in the team.
According to Celtic’s official website, De Vries has made just 15 appearances in all competitions for the Hoops so fat.