However, coach John Tortorella said Staal is still a possibility to rejoin the team abroad during their six-game stretch that includes four exhibition contests and two regular season games.
Tortorella said he expects to have an update on Staal's status within four to five days.
"We're going to try to get him on the trip," Tortorella said. "Once he feels better and we feel he can get into all the stuff we want him to do to get ready for the regular season, he'll come out."
As it stands, the Rangers will bring 10 defensemen on the team charter when they depart immediately following Monday's game against the Flyers in Philadelphia.
Those ten defenseman include mainstays Dan Girardi, Ryan McDonagh and Mike Sauer and several other blue-liners competing for spots: Michael Del Zotto, Steve Eminger, Tim Erixon, Brendan Bell, Dylan McIlrath, Stu Bickel and Blake Parlett.
"Everybody bumps up, everybody gets more of an opportunity," Tortorella said. "I guess that's the best way to put it."
Although Staal skated Sunday with the team, the 24-year-old missed practice Thursday and Friday to meet with specialists.
He'll continue to meet with specialists and receive treatment from the Rangers medical staff while the team is overseas.
"That's ongoing. We're not looking for results," Tortorella said. "It's just an ongoing procedure to try to help him."
When the team held Staal out of practice last week because of lingering post-concussion symptoms, the move sounded purely precautionary.
But the lasting effects from the concussion -- sustained after a crushing hit from his brother, Eric Staal, during a game against Carolina Feb. 22 -- now seem more alarming.
Tortorella would not rule out Staal for the team's regular season opener against the Kings in Stockholm, Sweden on Oct. 7, but the possibility he could miss some time seems more likely now.
"It's no secret that he's a huge part of our team and one of our top defensemen," captain Ryan Callahan said. "If we don't have him, it's going to be a huge hole."
Katie Strang covers the NHL for ESPNNewYork.com.