"There are definitely a few guys that I would love to see come over here," Berkman said. "You can't have everybody, but if J.D. came and said, 'Can you put a sales pitch on someone?' I would be more than happy to do it."
The Rangers have not reached that point yet. But with five weeks to go before Spring Training, Texas has not ruled out going after Bourn or Lohse, who are the top two free agents remaining on the market.
The Rangers have been reluctant to pursue either player to this point because of the perceived high demands being set forth by their agent, Scott Boras. But both players remain unsigned, with no landing spot in site.
The Rangers don't have a desperate need for either player. Daniels said the club would be happy if it ends up in Spring Training with the team it has now. But Daniels also acknowledged that the Rangers might be able to fit one more outfielder and starting pitcher into the mix.
"They are both areas that we would look at," Daniels said at the news conference to introduce Berkman.
Bourn is more likely to appeal to the Rangers than Lohse.
Bourn, 30, is a two-time All-Star and Gold Glove winner who played in 155 games for the Braves this past season, hitting .274 with a .348 on-base percentage, 96 runs scored and 42 stolen bases.
Bourn, who has played for the Phillies, Astros and Braves in his seven-year career, has led the National League in stolen bases three times and is considered a premier defensive player. But his .339 career on-base percentage is relatively low for a leadoff hitter. He was 10th in the Majors with a .346 on-base percentage in the leadoff spot this past season among players with 400 plate appearances at that spot in the order. Ian Kinsler was 17th with a .326 leadoff on-base percentage for the Rangers.
Right now, the Rangers are planning to go with a platoon of Craig Gentry and Leonys Martin in center. Martin, who turns 25 in March, remains a highly regarded prospect who hit .359 with 12 home runs, 42 RBIs, a .422 on-base percentage and a .610 slugging percentage in 55 games at Triple-A Round Rock this past season.
Signing Bourn would likely keep Martin from being an everyday player, but that may only be for one season. Both David Murphy and Nelson Cruz are free agents after this year. The Rangers don't want to do a mega-deal for Bourn, but they might consider something on a short-term contract.
"As we sit here right now, we set out our Spring Training roster today, and with the exception of some internal invites, we don't need to make any other additions," Daniels said. "We're ready to go with our club as is. With Nellie and Murph and all the guys we've got internally who we like in center field, we're real comfortable with our outfield."
The Rangers are also comfortable with four of the five spots filled in the rotation by Matt Harrison, Yu Darvish, Derek Holland and Alexi Ogando. The fifth spot is still open. Martin Perez finished last season as the fifth starter, but he was 1-4 with a 5.45 ERA in six starts and six relief appearances.
Justin Grimm, who was 1-1 with a 9.00 ERA in two starts and three relief appearances, is another fifth-starter candidate, and the Rangers are considering the possibility of moving Robbie Ross from the bullpen to the rotation.
Lohse is 34, but he is coming off an outstanding season. He was 16-3 with a 2.86 ERA in 33 starts and 211 innings for the Cardinals in 2012, and 14-8 with a 3.39 ERA in '11. Berkman, who played with Bourn in Houston, was Lohse's teammate for two years in St. Louis.
The unknown for the Rangers is Colby Lewis, who underwent surgery to repair a torn flexor tendon in his right arm on July 27. The Rangers have been getting good progress reports from their medical staff and are hopeful Lewis could be back before the original June 1 target date. That would lessen the need for a fifth starter, but the Rangers found out last season what happens when a rotation is hit hard by injuries.
"Much like the outfield, we have our four starters relatively set," Daniels said. "We've got really good news on Colby. If we don't add another starter on a guaranteed contract, you're looking at Martin Perez, Justin Grimm, Robbie Ross, maybe some others, maybe somebody on a non-roster deal competing for that spot. Or we could go in and add a guy on a guaranteed deal, in which case, when Colby comes back, we have a great problem."
The Rangers were willing to pursue free-agent starter Zack Greinke because they felt he is an impact No. 1 starter. Boras said at the Winter Meetings that Lohse fits that description as well. Greinke signed a six-year, $147 million contract with the Dodgers. The Rangers will not go anywhere near that for another starting pitcher.
But there are still two prominent free agents sitting out there the Rangers haven't ruled out.