"I was told late this morning that Daniel had a desire to come back and play for the Senators," general manager Bryan Murray said on the team's website. "So we now have an opportunity to negotiate with JP Barry, his agent and see if we can get a contract that should allow that to happen."
Alfredsson, 40, had a salary-cap charge of $4.875 million in 2012-13, the final season of a four-year contract that started in the 2009-10 season. Murray said he hoped to begin talks on a new deal for Alfredsson sometime over the weekend.
"JP was traveling today so I really didn't have a chance to get any other information other than Daniel informed him that he would like to play and that we should start talking," Murray said. "That will start hopefully sometime over the weekend, and we'll see where it takes us. Hopefully we can get a deal done fairly quickly."
Earlier Friday, Alfredsson told a Swedish reporter that after taking some time off he felt a desire to return.
"I needed a few weeks to see if the necessary urge for summer training and pre-camp was there," he said. "And it is."
Alfredsson, captain since the start of the 1999-2000 season, led the Senators in scoring with 10 points in 10 games in the Stanley Cup Playoffs. He tied for second on the Senators with 10 goals and was third with 26 points in 2012-13, playing 47 of 48 games.
Taken by the team in the sixth round of the 1994 NHL Draft, Alfredsson is the franchise's all-time leader in games played (1,176), goals (426), assists (682) and points (1,108). He's second in goals and third in points among Swedish-born NHL players.
Alfredsson said though the chance to play for Sweden in the 2014 Olympics in Russia wasn't a driving force to his return, the opportunity to represent his country at the Games for a fourth time would be something special. He had team-highs of five goals and 10 points in eight games to help Sweden win the gold medal at the 2006 Games.
"The chance to maybe play one more Olympics wasn't part of my decision to continue but I'd like to, of course," he said.