"There is still no final decision on anything, but we had a very good conversation," Murray told the Ottawa Citizen on Thursday after speaking with his captain last week. "We did talk about the team, what has happened around the team. There was interest on his part in what was going on."
Alfredsson, who turns 40 this December, is spending the offseason in his native Sweden. He had 27 goals and 32 assists in 75 regular-season games before scoring two goals during Ottawa's first-round playoff loss against the New York Rangers.
Murray did not ask Alfredsson if he plans on hanging up the blades this summer. Instead, he has his fingers crossed that No. 11 will be a participant when training camp opens in September.
"I'm not going to ask that question," Murray said. "But the impression I got was a good one."
Alfredsson has 416 goals and 666 assists in 1,131 regular-season games. He's added 47 goals and 43 assists in 111 playoff games. Alfredsson helped the Senators reach the Stanley Cup Final in 2007.
"It's a tremendous hole if he doesn't play," Murray said. "But we're fine as far as having numbers."