According to a recent report in The Glasgow Evening Times, Bayer Leverkusen are interested in signing Ambrose from Celtic in the summer transfer window.
It has been reported that the Nigeria international defender is high on the German club’s transfer list.
It has also been claimed that Bayer, who finished third in the Bundesliga last season and will feature in the Champions League during the 2016-17 campaign, could make a bid of £1.5 million to secure the services of the 27-year-old.
Former Celtic striker Sutton believes that the Bhoys should sell Ambrose, who can play as a central defender or as a right-back.
“I still have concerns about the defence and I see Efe Ambrose has made his way out to Slovenia,” Sutton wrote in The Daily Record.
“Efe is a nice bloke but if Bayer Leverkusen have offered £1.5million for him Celtic should charter a plane for him out to Germany.
“It’s too big a risk to count on him in these qualifiers. Erik Sviatchenko looks decent but he needs someone with real presence alongside him.”
Ambrose has been on the books of Celtic since 2012, but he could struggle to play regularly for the Bhoys next season.
The former Ashdod defender is prone to making mistakes, and new manager Brendan Rodgers should be looking for someone more reliable to play regularly in that position.
Celtic have already started pre-season training and will feature in the Champions League playoffs soon.