The Belgian international was on the club’s radar earlier this month, along with Norwegian right-back Omar Ellabdellaoui and Fernando Fonseca while a host of other full-backs were loosely linked with a Parkhead switch.
The Hoops have this week turned their attentions to out-of-favour Borussia Dortmund right-back Jeremy Toljan, with reports in Germany suggesting a loan move to be imminent.
But reports in the Italian media claiming Celtic made a fresh attempt to prise Castagne from the Serie A side are wide of the mark, with club sources confirming no bids have been lodged for the 23-year-old.
Castagne has started Atalanta’s last five games in a left-wingback role, helping them record three wins and two draws. He scored in the last match, a 3-3 draw with Roma.