AC Milan midfielder Andrea Pirlo suffered a calf strain in training this week and will be out of action for two to three weeks.
Cossu is not part of the 23-man squad for the World Cup, but can be added as a replacement until the June 13 deadline.
“In conjunction with the medical staff we have decided to take him along,” explained Italy coach Marcello Lippi.
“If Pirlo skips three games, it’s not a problem. He might come back in the fourth, who knows?
“For the rest I can tell you only Cossu will come along with the group, as whatever happens I won’t be calling any more players.”