"He'll make the decision when he's ready," a league source told the paper. "He needs time."
Alfredsson, 40, is scheduled to become an unrestricted free agent July 5. He will either sign a one-year deal with the Senators or call it a career.
In 47 games with the Sens last season, Alfredsson has registered 10 goals and 16 assists for 26 points. He won the Mark Messier Leadership Award on Friday.
"I've just allowed myself to take it easy, spend some time with the family, to relax, get a feeling of how my body feels, how I feel," Alfredsson said.
The Sun claims Alfredsson will likely earn around $4.5 million next season if he does choose to return.
"I haven't pursued that and I'm not going to until he tells me he's ready to talk about it," Senators GM Bryan Murray told the Sun.