"I guess it's the big issue in town now," Murray said. "I didn't realize it was that big an issue because we're going to get it done, I would assume."
Alfredsson started the offseason unsure he wanted to return for his 18th NHL season, but late last month announced his desire to do so.
Since then, he has spoken to teams other than the Senators, with TSN and ESPN.com's Pierre LeBrun, and the Ottawa Sun, reporting Thursday the decision will be made between the Senators, Boston Bruins or Detroit Red Wings.
The unrestricted free agent can sign as of Friday. Murray said he spoke to Alfredsson's agent, J.P. Barry, Wednesday afternoon about a possible one-year contract.
"I have not heard the dollar figure at this point," said Murray, who expected to hear from Barry again Thursday.
Murray said he told Barry, "Talk to [Daniel]. Ask him how much [money] he needs to play in Ottawa."
Asked if he was afraid Alfredsson would play elsewhere, Murray said, "Nobody's ever said that to me, other than I heard it on TV and on the radio."
Alfredsson had 10 goals and 16 assists in 47 games during the 2012-13 season. He had four goals and six assists in 10 Stanley Cup Playoff games.
Alfredsson, Senators captain since the start of the 1999-2000 season, is the franchise leader in games played (1,176), goals (426), assists (682) and points (1,108). He's second in goals and third in points among Swedish-born NHL players.
"We gave it our best pitch," Murray said.
Clarkson turned down an offer from the Devils over the weekend. Murray said he was told the wing would investigate "five or six" options.
"He's competitive, gritty, tough, last full season he got 30 goals; last year he led the Devils with 15," Murray said. "We hope that he chooses us; unfortunately we don't dictate all of it. He'll have, I'm sure, a number of options, but he is one person we have targeted and he fits the role that we're really looking for."