Sources told ESPN on Friday that Crosby was held out of the 5-3 loss with a concussion. The Penguins have only said that he suffered an upper-body injury after taking a high hit from Rangers defenseman Jacob Trouba in Game 5 on Wednesday.
Crosby participated in the optional practice and did not wear a non-contact jersey, but Sullivan would not say if his star has been cleared for contact. Crosby also skated individually on Friday with skills coach Ty Hennes.
Crosby had nine points in the first five games against the Rangers.
Also returning to the ice Saturday was starting goaltender Tristan Jarry, who has yet to play in this playoff series due to injury, and winger Rickard Rakell, who hasn't played since Game 1 after taking a hard hit.
Sullivan did tell reporters that all players would be traveling to New York for Game 7 on Sunday.