The centre-back once again showed his value to Ange Postecoglou’s side on Sunday with a man of the match display in the 2-1 victory over Rangers, including netting the winner.
Currently on loan from Tottenham Hotspur, his form has attracted interest from Premier League sides.
According to the Daily Record, Burnley, Wolves and Leicester City are all keen on Carter-Vickers.
The 24-year-old remains under contract at Spurs beyond the summer and will command a significant fee.
Former Celtic and Spurs star Raymond Vega believes the Scottish league leaders should be willing to break the bank for the US international if it means paying up to £10million.
With him impressing north of the border, Vega expected Spurs and Daniel Levy to drive a hard bargain.
"Cameron is a brilliant defender and I have no doubt he should stay at Celtic,” he told the Scottish Sun.
“Should they sign him permanently? Absolutely. People are talking about £10m, but Celtic should pay that to keep him.
“Knowing Daniel Levy, he will want top dollar for Cameron as he always looks to get the best deal for Spurs.
“Are Celtic prepared to do that? He is a top player, and even if they have to pay a little bit over the odds for him, then I think they should.
“He’s a massive asset to the club already, but I think if he was there permanently he could get even better."