Murray is trying to acquire a top-six forward and move up in the Draft. The Senators currently select 17th.
"We have a chance to get a good player this year. The draft, through the first round, is fairly decent," Murray told the Sun. "There's a variety of types. We know now that we've got a core of young players coming with a fair amount of talent.
"There's a certain type of player that we'll be looking for in that spot. It's hard to say at the moment what that is, but a player who is going to fit into our hockey team in the future."
Murray is planning on taking advantage of Wednesday's GM meetings in Boston to speak face-to-face with some of his counterparts about making moves. He's admitted to already speaking with four teams, all pegged to draft ahead of him, about moving up.
The Sun claims the Senators are willing to trade one of their top young prospects as part of a package to move up in the draft.
"I will call a number more and see if anybody wants to move," said Murray. "There are certain reasons to move fairly high and if you don't do that, then maybe we're OK where we are."