Rangers general manager Jon Daniels and his top assistants, Thad Levine and A.J. Preller, are busy looking into opportunities this week. They are attending the General Managers Meetings in Indian Wells, Calif., and Ryan said there is a possibility they could meet with Hamilton's agent, Michael Moye, while they are there.
Hamilton became a free agent at the end of the World Series and is free to sign with any team. Hamilton has indicated all along that the Rangers will have the last chance to sign him at the end, and Ryan said that's still the informal agreement.
"I just don't think we can wait around until January," Ryan said. "But I think people will have a better idea of where that's headed after this week."
Ryan said he has "no idea" where Hamilton will end up. He said people have a pretty good idea of what the annual salary will be, they just don't know the length of the contract. The annual average salary could be in the $20-25 million, but the length could be anywhere between five and 10 years.
Hamilton, 31, hit .285 with 43 home runs, 128 RBIs and a .577 slugging percentage for the Rangers this season. But he does have a history of injuries that could make clubs reluctant to give him a 10-year deal that Albert Pujols signed with the Angels last winter or the nine-year contract that Prince Fielder signed with Tigers.
"That's the question," Ryan said. "I think everybody has a feel for what the dollars are going to be. But when you get into these big long contracts, each club just has to determine what your tolerance is going to be."
Ryan is not keen on long-term contracts, but he's less reluctant on position players than he is on pitchers.
"Obviously position players are somewhat different than pitchers because if they do sustain an injury, it's usually not a career-threatening injury," Ryan said. "But when you get into an extended long-term contract for anybody and something goes wrong, it can be crippling for a ballclub. That's what you've got to look at."
If Hamilton signs elsewhere, the Rangers are not going to be able to completely replace his offensive production. Ryan said the club would have to look for a left-handed bat to help balance out a predominately right-handed lineup.
But the Rangers could look for other ways to improve their ballclub, and Greinke figures prominently in their plans. The Rangers are among the teams who will go hard after Greinke this winter and Ryan suggested he has less concerns about him breaking down than some of the other free-agent pitchers out there.
"When I look at him, he's got a real feel for pitching," Ryan said. "He has good command and a really good changeup. When I look him at him, I don't have as many concerns about him breaking down. He has a good delivery, effortless. You probably feel stronger about him holding up than some of the power guys. That's my initial thoughts."
Greinke, 29, was 15-5 with a 3.48 ERA in 34 starts and 212 innings for the Brewers and the Angels this season. He had some issues with social anxiety disorder early in his career, but has overcome those and been one of the most durable pitchers in the Majors over the past five years.
He is one of 17 pitchers who have averaged over 200 innings per season in the last five years. He missed a month at the start of the 2011 season because of a fractured rub incurred in a pickup basketball game, but has stayed away from significant arm problems.
"If we can strengthen our rotation, we'll look to do that," Ryan said. "Do I think it's a possibility? It's too early to predict. You have to look at what's available on the trade market and the free-agent market."
The Rangers are looking hard and they are eager to do what they can to improve the ballclub. That could mean re-signing Hamilton. But the Rangers aren't waiting around as if that's the only possibility.