They also remain interested in West Bromwich Albion’s Scotland winger Oliver Burke.
That move could be accelerated if the Baggies manage to get James McCarthy on loan from Everton.
There is still a possibility of high-profile departures this month.
Belgian defender Dedryck Boyata is out of contract in the summer and won’t be signing a new deal.
Celtic transfer news: Vakoun Issouf Bayo (left) could cost £2.3m (Image: GETTY)
Celtic transfer news: Brendan Rodgers will come in with a £2m bid for Vakoun Issouf Bayo (Image: GETTY)
Turkish side Besiktas have been linked with a January bid.
Captain Scott Brown’s long-term future is also up in the air.
He is in the last five months of his contract and while he has been offered a one-year extension, he has strong interest from new A-League side Western Melbourne.
They’ve discussed a lucrative three-year deal but the Aussies would also have to pay a fee to land Brown this month.
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Asked by Express Sport where he wants Celtic to strengthen, the former manager said: “The question is whether Celtic can actually get better players than they already heave.
“I don’t think top young players in the Premier League are going to leave to go to Scotland now.”
Barnes has also warned Rodgers cannot become complacent in the transfer market.
And the boss may have to offer his players the chance to challenge themselves.
“It’s been so easy for them that it’s difficult to maintain that level of football,” Barnes said.
“Look at Bayern Munich, it’s the same thing that they’re going through, where you win so confidently week in week out, but the harmony isn’t right.
“Boyata wanted to leave in the summer, Dembele left, so having players who are happy to be there and who have something to prove will play with an intensity to show that.
“A lot of them are like ‘well, do I really want to be here?’ and the harmony is so important.”