The 31-year-old is out of contract at the end of the season, but it is understood that the Serie A club have offered him a new two-year deal.
However, Chivu's agent Victor Becali has claimed that the Romanian is still "reflecting" on the offer.
"We are reflecting; we have not made any decisions yet. We won't make Inter wait too much longer, though. I assure you that by the end of the week we will communicate our decision. I cannot say any more for now," he told FCInterNews.it.
Chivu joined Inter from Roma in 2007.