Lyon's agent, Barry Meister, said late Monday night that he'll continue to talk with the Tigers about a contract, refusing to close the door on a return for his client. Detroit, too, wasn't writing off the idea of talking with either free agent.
For now, however, the Tigers are left without an experienced closer in their bullpen for the time being.
When asked earlier Monday, Dombrowski indicated he didn't have a feeling whether the team would go with experience or youth in the closer's role next year.
"We're talking about a lot of different things right now," Dombrowski said. "And there's still a long time to go in the winter. Last year, I guess we didn't sign Brandon Lyon until January, and we didn't know if it was going to be Lyon or Rodney as our closer.
"We've got [Joel] Zumaya as a wild card. I've been talking to our trainer, and [Zumaya] feels great at this point. I don't know which way we'll go, but I think we'll have enough people out there that will determine that. Somebody always closes games for you."
Rodney closed out 37 saves for the Tigers last season, to go with a 4.40 ERA and 75 2/3 innings. The 32-year-old is expected to be one of the more valued closers on the market, in part because he will not cost teams a Draft pick to sign. Detroit would receive a compensation pick near the end of the second round if he signs with another team.
Lyon saved just three games for Detroit, but his 2.86 ERA and 56 hits allowed over 78 2/3 innings made him one of baseball's more valuable setup men. Like Rodney, he's a Type B free agent, earning the Tigers a compensation pick if he signs elsewhere.
Jason Beck is a reporter for MLB.com.
This story was not subject to the approval of Major League Baseball or its clubs.