For now, though, Lyon will field offers from other teams after Nov. 13, when they can discuss specific dollar figures with him. Until then, teams can discuss contracts in general, but not specific terms.
"Brandon would be thrilled to come back to Arizona," Meister said. "We're going to get some sense of the market and come back to Arizona and have a meeting of the minds. I don't think it would be surprising if he got some multiyear offers from teams."
Lyon was the D-backs' closer until being taken out of that role on Sept. 13. The right-hander was dominant from April 9 to June 12, when he tossed 25 scoreless innings over 24 appearances.
Struggles in the second half of the season finally cost him his closer's job, as Arizona manager Bob Melvin replaced him with Chad Qualls. Lyon finished the year 3-5 with a 4.70 ERA and 26 saves.
During the season's final week, Melvin said that Qualls had the inside track to be the team's closer heading into Spring Training in 2009.
That doesn't sound like it would be a hindrance, at least from Lyon's point of view, to him returning.
"I think he's willing to consider a closer's role or an eighth-inning role, depending on the situation," Meister said.
Whether the D-backs will choose to match either in years or dollars what Lyon could get on the open market remains to be seen.
Steve Gilbert is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.