Source: White Sox claim Manny Ramirez

The clock started ticking on Manny Ramirez's future as a Dodger on Friday, when the Chicago White Sox were awarded a waiver claim that gives them exclusive rights to make a deal to acquire Ramirez over the next four days.

The teams have until 1:30 p.m. ET Tuesday to complete a trade.

According to a source monitoring the waiver wire, the White Sox were one of three teams to claim Ramirez after the Dodgers placed him on trade waivers Wednesday.

The Texas Rangers also claimed the 38-year-old future designated hitter, a source told ESPNDallas.com's Richard Durrett.

And there were strong indications the other team to claim Ramirez was the Tampa Bay Rays. But the White Sox had first dibs because they had the lowest winning percentage among the American League teams that put in a claim. None of the other 15 National League teams claimed him.

Ramirez was not in the Dodgers' starting lineup Friday against the Rockies, raising further speculation he could be on his way out of Los Angeles, although Dodgers manager Joe Torre insisted he didn't start Ramirez because of a tough matchup against Rockies ace Ubaldo Jimenez.

"It's a couple of reasons," Torre said. "One is he hasn't played that much, and Jimenez is tough. The other one is that he is 1-for-13 with six ... strikeouts against him."

Torre said he plans to start Ramirez on Saturday night.

"My guess is yeah," Torre said.

Now that the waiver portion of the process is out of the way, there are four potential outcomes between now and Tuesday:

• The Dodgers and White Sox could work out a trade in which each team pays a portion of the approximately $4.4 million remaining on Ramirez's contract this year, and the White Sox send a player or players to the Dodgers in return.

"It's somewhat of a gamble if you are willing to step out there like we sometimes are," White Sox general manager Kenny Williams said Friday night, speaking generally about potential moves to improve the team. "Like we often are, in the situation we are. In a two- or three-day period, you can find yourself further back and wonder whether or not you've done the right thing."

• The Dodgers could simply let the White Sox take Ramirez and assume all of his salary, most of which ($3.3 million) is deferred.

• The teams could work out a deal, only to have Ramirez opt not to waive his no-trade clause and veto the deal. That's viewed as unlikely, but there have been reports this week Ramirez could ask for a contract extension in order to approve any trade.

"Generally speaking, you approach the player only when you have a deal in place," Dodgers general manager Ned Colletti said. "I'm just talking in total generalities, not about any specific player. There are a lot of players who have been claimed by a lot of teams, and I would say 95 percent of them are still with the club that put them on waivers."

• The Dodgers could decide they're too close in the wild-card race to trade away their No. 3 hitter and pull Ramirez back. The Dodgers finished sweeping three games in Milwaukee to pull within five games in the wild-card race, and they still have four games against teams ahead of them in that race -- Colorado and Philadelphia -- before the Tuesday deadline.

Until the past several days, a Ramirez deal appeared inevitable, once he returned to the active roster following a stint on the disabled list for a calf injury. But the Dodgers, who had been eight games back in the wild-card standings and 12 behind in the NL West as recently as Sunday, might have changed their front office's thinking with their first series sweep since the last week of June.

Speaking with reporters in the dugout before Friday night's game at Colorado, Colletti gave no indication as to whether he was on the verge of trading Ramirez to the White Sox, according to ESPNLosAngeles.com's Tony Jackson.

Colletti told USA Today earlier this week that he was "not inclined" to trade any players at a point when the Dodgers are on the fringes of contention for a playoff spot.

Asked about that comment Friday, Colletti said, "That was where I was at the time."

Asked where he is now, Colletti said, "I'm in the same place right now."

Asked what could possibly change that before next week, Colletti said, "How we play."

Other teams that have spoken with the Dodgers said they've shown no inclination to trade any of their veteran players this month -- and have consistently told those clubs they wanted to wait to see where they were in the standings at the end of August.

So the club held off until Wednesday to place Ramirez on waivers in order to give itself the most possible time to consider its options. One source who spoke with the Dodgers reported they saw "no reason to rush" to trade Manny or anyone else, until they get a better feel for whether they're legitimately in contention. So it would be surprising if they made any final decision on Ramirez either way until the deadline approaches.

White Sox manager Ozzie Guillen was asked Friday how adding Ramirez would affect team chemistry.

"If this kid comes here, we have rules and we're going to go by the rules. Jerry [Reinsdorf] has his rules, Kenny [Williams] has his rules and the team has its rules," Guillen said. "My rules are going to be done because we've had the same rules for a few years and he's got to go by it. I will talk to him like I talked to Ken Griffey Jr. and like I've talked to guys coming to this ballclub and what I like to do. Believe me, if this kid comes here, it's because he wants to. That's a good thing."

Guillen had already given some thought to how he'd play Ramirez.

"I have to see him. He can DH, hopefully he can play a little bit in the outfield," he said. "Manny only plays left field, and I've got a good one playing right now. I'm not going to take any at-bats or any playing time from Juan Pierre to give Manny."

Jayson Stark is a senior writer for ESPN.com. Richard Durrett is a reporter and columnist for ESPNDallas.com. Tony Jackson covers the Dodgers for ESPNLosAngeles.com. ESPNChicago.com's Doug Padilla contributed to this report.