Neymar enjoyed a fruitful four-year spell with the Catalans earlier in his career, winning two LaLiga titles and a Champions League, as well as helping form one of the world's most-feared attacking trios alongside fellow South Americans Luis Suarez and Lionel Messi.
However, he then shocked the world by swapping the Camp Nou for the Parc des Princes in July 2017 for a then world-record €222m fee.
There had been rumours in the Spanish press that the Samba star had grown tired with life in the French capital and was pining for a move back to his former club, but Cardoner has now moved to quash those reports.
"No one on the Barca board has talked about the possibility of bringing back Neymar, right now we can't give an answer because no one has even mentioned it," he told Spanish radio station 'SER Catalunya'.
"He was the one who left, it would be different if we hadn't believed him and now we wanted to bring him back, but that's not the case.
"If we did want to sign him then the board would have to discuss it but until now no one has talked about it."