The 23-year-old right-back has been capped two times by the Belgian national team and Hoops boss Brendan Rodgers sees him as a long-term replacement for Mikael Lustig.
Celtic’s first choice right-back of the past few seasons is out of contract at the end of the campaign and has previously been linked with a move back to his native Sweden with AIK Stockholm.
Castagne appears to be open to the idea of moving on from his current side, Italian Serie A club Atalanta, after becoming frustrated at his lack of first-team opportunities this term.
He accused manager Gian Piero Gasperini of failing to properly communicate and claims he has a better relationship with national team coach Roberto Martinez.
He said: “I speak more with Martinez in one day than in a year-and-a-half with Gasperini. I need playing time to stay and everything can go very fast in football.”
Despite this Atalanta are said to be uninterested in selling their player during the January window.