Meanwhile, his general manager waits for the news of whether the long-time captain plans to return for another season.
"We have talked, I've talked to Alfie in the past couple of days," Senators GM Bryan Murray said at a press conference Tuesday announcing the renaming of the team's arena as the Canadian Tire Centre. "I told him to take whatever time he needs and come back to me when you can -- as early as you can, that would help me -- but do whatever you have to do to satisfy your family to make sure you're ready to play."
Alfredsson, 40, has played 1,178 games for the Senators, scoring 426 goals and recording 682 assists for 1,108 points. In the 2012-13 season, Alfredsson recorded 10 goals and 16 assists in 47 regular season games, and added another four goals and six assists in 10 Stanley Cup Playoff games.
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He's set to become an unrestricted free agent next month.
When previously asked by reporters if he would return for an 18th NHL season, Alfredsson said he had yet to consider his future.
"I feel my game is good enough and I can keep up and I don't feel like I don't have it anymore," the 5-foot-11, 203-pound center said at the Senators' end-of-season media availability.
The father of four young children, Alfredsson said his choice will be a family decision, ultimately hinging upon whether he is up for a summer of training and another long season.
"It's been a mentally draining season with the schedule and everything and I just feel like I need to give it a bit of time and freshen up and take it from there," he said.
If his teammates have anything to say about it, Alfredsson will be postponing retirement for a while.
"We're definitely going to pressure [Alfredsson] to help his decision along," forward Jason Spezza said. "He's going to need a bit of time, but we're hoping he's going to come back for sure."
Were Alfredsson not to return, Ottawa would have a large pair of skates to fill on the ice and in the locker room.
"Obviously he fills a vital role on this hockey team," Murray said. "Number one, he's a top-six forward, he's a point-getter, he's much more than that, however. He's a leader, he's 'the glue guy' in the room, he has a respect level among our young guys -- and we have many of them -- that really allows us to play players that we didn't know if they were ready to play, but they come in and play and contribute because Alfie shows them how to work, shows them how to practice and, through his conversations with them, allows them to be confident enough to go out on the ice and play."
If Alfredsson elects to retire, Ottawa will look to re-purpose the money allocated for him elsewhere, but Murray knows replacing a player of Alfredsson's caliber is no small task.
"In a budget you have to have certain dollars put aside for certain players and hope that works and if you don't get that player then you hope that you find someone," he said. "We're not going to get that type of player, we know that. The intangibles he brings alone are way above anything I suspect I could get."