Gomez, 33, is not expected to sign for more than $1 million, but has attracted the interest of several other clubs.
A source with knowledge of the situation told TFP the Ducks' interest was fairly mild and talks did not continue throughout the night. It's possible Murray resumes talks with Gomez's camp this morning.
If the Ducks decide Gomez isn't the right fit, they could go claim center Tim Connolly, whom the Toronto Maple Leafs placed on waivers yesterday.
Connolly, 31, is in the final year of a two-year contract with signed with the Leafs last summer.
While he's set to get paid $4 million (just over $2.34 million prorated) this season, his carries a salary cap hit of $4.75 million.
If, however, Connolly clears waivers by noon ET today and the Ducks remain interested, they could trade a draft pick for him and have the Leafs pay a portion of his salary.
Earlier this week, the Leafs traded center Matthew Lombardi to the Phoenix Coyotes in exchange for a conditional 2014 fourth-round pick, and are paying a portion of his salary as part of the deal.
If the Ducks come up empty on both Gomez and Connolly, Murray will continue to explore other trade options.