Rangers general manager Jon Daniels made it clear that, "We want him back."
But early discussions between Daniels and agent Sam Levinson have not been particularly productive, leading to the distinct possibility that Byrd will be playing elsewhere in 2010.
"I told my agent I want to be in Texas," Byrd said Friday. "I told them if there was anything of substance with the Rangers, give me a call. They haven't called me.
"At this point, I have no idea. I'm not pessimistic until the Texas Rangers say, 'We don't want you.' I'd say it's 50-50 up in the air. I was more optimistic at the end of the season. I thought we would get something done at the end of the season like the Angels did with Bobby Abreu. But I guess they are looking at other options."
The Angels and Abreu reached an agreement earlier this month on a two-year, $19 million contract with a $9 million option for 2012. Abreu, who made $5 million on a one-year deal in 2009, hit .293 with 96 runs scored, 15 homers and 103 RBIs.
Byrd hit .283 with 66 runs scored, 20 homers and 89 RBIs for the Rangers while playing what manager Ron Washington said was Gold Glove-caliber defense in center field. He can also play left and right field.
"I think I have a good chance to find a place to play based on what I've done in Texas the past three years and being able to play all three positions," Byrd said. "I think a lot of other teams are looking for an outfielder with versatility who can play all three positions."
Byrd has made no public contract demands other than he would like some kind of multi-year deal.
"If people offer me a contract at two years and the right numbers, I'll sign," Byrd said. "If people offer me three years at the right numbers, I'll sign.
"I'm not interested in a one-year deal. Do I want a three- or four-year deal, yes. But I don't know what will happen. Last year, I thought Orlando Hudson would get a five-year deal, and he ended up getting one year and an option. The more seasons the better, but I just want fair value."
There are a number of teams that are looking for outfield help this winter, although most of them are looking for a corner outfielder.
The Red Sox will need a left fielder if they can't re-sign Jason Bay and the Cardinals will be in the same situation if they can't re-sign Matt Holliday. The Yankees could lose Johnny Damon and Hideki Matsui, putting them in a position to need outfield help.
The Blue Jays and the Pirates both want a corner outfielder with some power. The Giants just need overall offensive help for their premier pitching staff. So do the Tigers. The Mariners, Mets, Braves and Reds are looking for a left fielder that can hit. The Nationals want a bat in right field.
The question is if other teams look at Byrd as a center fielder, corner outfielder or a fourth outfielder. But his .811 OPS (on-base plus slugging) was 27th among 72 batting title-qualifying outfielders in 2009 and is fourth among current free-agent outfielders.
Byrd has also hit a combined .294 in three seasons with the Rangers. That's the 17th highest among 98 outfielders with at least 800 at-bats over the past three seasons.
"I don't know what my worth is on the market, but I guess I'm going to find out," Byrd said. "I didn't want to find out. I wanted to be in Texas."