According to the Sun, he plans on speaking with Senators GM Bryan Murray and head coach Paul MacLean, as well as his wife Bibi, before deciding whether he'll play next season.
"We'll have our meetings. Then I'll take some time," Alfredsson said. "I'll talk to (Murray) to see what he thinks, what timeline and then go from there.
"All I can say is it's been a great year in terms of the group we had, the adversity we faced. We've become a tight group. We stuck together all along. It's been a lot of fun. I'll definitely take that with me when I think about what to do."
MacLean indicated that Alfredsson will be back with the organization in some capacity next season, whether or not he'll be on the ice.
"I don't want to speak for him, but usually those decisions take some time and he'll let us know in good time," MacLean told the Sun. "I understand the difficulty for him and his family. He's a tremendous person, a tremendous father and he just happens to be a pretty good hockey player."
Alfredsson picked up 10 goals and 16 assists for 26 points in 47 games with the Sens this season.
The native of Gothenburg, Sweden, has played in 1,178 career NHL regular-season games over 17 seasons with the Senators. He has accumulated 426 goals and 682 assists for 1,108 points, along with 500 penalty minutes, over his career. He was originally drafted by the Senators in the sixth-round (133rd overall) of the 1994 NHL Entry Draft.
"My wife takes a heavy load at home, and without her I would never be able to play this long," said Alfredsson. "At times, I definitely feel like I miss out at home. You miss a lot of stuff. The first goal in your son's career, birthdays. But ... this game has given me so much, on and off the ice. When I make the decision I know it's definite, and that's why I want to take some time."