Sivivatu, 27, already ruled out of this weekend's Super 14 final against the Bulls at Pretoria, is to see a specialist this week, the New Zealand Herald said.
Sivivatu injured his left shoulder in a tackle late in the 14-10 victory over the Hurricanes.
This is the second time this season that Sivivatu has injured the shoulder and if surgery is prescribed, will be out for about six months.
Crusaders halfback Andy Ellis could also be out of the reckoning for All Blacks' selection this season.
Ellis played the last six weeks with three fractured ribs and will now need up to 10 weeks for them to heal.
Ellis fractured the ribs in the round seven win over the Stormers in Christchurch.
"Because I haven't given them a chance to re-heal I just fracture them again each week. I've been getting through with a local jab into them," Ellis told the Stuff website after the Crusaders 23-36 semifinal defeat to the Bulls in Pretoria.
