Barca are in advanced talks with Roma over a fee for the Romania international, which could see Ludovic Giuly move to Italy as a makeweight in the deal.
However, Marca says Chivu favours a reunion with his former Roma coach, Fabio Capello, and should the Italian be confirmed as Real boss for next season he would jump at the chance of playing for the Italian at Madrid.
Chivu is yet to agree personal terms with Barca and is putting off talks until he knows the situation of Capello at Real.