The 39-year-old was reportedly going to meet with Senators GM Bryan Murray and coach Paul MacLean prior to the NHL Awards, which take place on Wednesday night in Las Vegas.
Once the Sens were eliminated in the first round of the playoffs by the New York Rangers back in April, the captain had hinted that his decision would take a few weeks.
After playing for Sweden at the World Championships at the start of May, Alfredsson restated that his choice was forthcoming, though he revealed on Tuesday that an illness has played a role in holding up his decision.
"It's like any job in the world; you go through ups and downs. As you get older, it's a physical game and to handle that and don't feel too banged up when you do retire -- you still want to be able to play with your kids -- there are so many factors that come into it."
In 75 games with the Sens this past season, Alfredsson collected 27 goals and 32 assists for 59 points.