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.