As a result, a number of teams have been knocking on his door, including the Boston Bruins, Detroit Red Wings and San Jose Sharks.
While it would be a surprise to many to see Alfredsson sign outside of Ottawa, the Sun claims he could announce his decision as early as Thursday.
According to the paper, the Senators are working on a one-year deal with Alfredsson, but the two sides are trying to hammer out the dollar amount. The Senators are hoping to sign their captain to a deal closer to $4 million, while other teams could offer as much as $6 million.
"I don't know if his price goes by the market activity. He's, from what I know, about him, I mean, he's a pretty principled guy," said Bruins GM Peter Chiarelli. "In the sense that he is a very focused guy, if he wants to go somewhere and play or stay in Ottawa, it's not about the money."