Barella has been linked with some of Europe's biggest clubs.
“It's a dream to keep Barella, but to be perfectly honest, I'm not sure if it's achievable," director of sport Carli told GianlucaDiMarzio.com.
“There are two Italian clubs who want him. We'll see… We already turned down many offers last year, such as over the summer from Atletico Madrid.
“As things stand today, I really don't know if he will remain or not. There is no guarantee he'll stay, but in January we didn't take any proposals into consideration.
“If he were to leave, we'd have to find a suitable replacement. Nicolò is a professional who really cares about Cagliari, so he just has to focus on finishing this season as well as possible.
“We'll try to consolidate and reinforce the squad. I believe there are at least two or three players who haven't fulfilled their potential yet, among them Ragnar Klavan, Valter Birsa and Lucas Castro. They'll be like new signings next season."