CHICAGO -- Ryan Dempster's next start for the Cubs would likely be Tuesday at Wrigley Field, with first pitch scheduled four hours after the Trade Deadline ends. Will he face the Pirates that night or be in another uniform?

The Cubs hope Matt Garza can start Monday. Could that be his last start for the team?

What about Bryan LaHair, Jeff Baker and Reed Johnson? The Cubs have had inquiries about a lot of their players, and teams looking for that extra bat -- Johnson has an attractive .329 average against left-handed pitching -- may try to make a deal before Tuesday's Trade Deadline.

Is it any wonder the Cubs' players changed the channel on the clubhouse TV in Pittsburgh this week when MLB Network started discussions on trade rumors?

"You don't want to be a seller," Cubs general manager Jed Hoyer said. "All the guys on your team sit there and look over their shoulder. I think everyone exhales after the Deadline for that reason."

Dempster may not be able to breathe until Tuesday night. He apparently eliminated the Braves. Atlanta general manager Frank Wren had a proposal in place, but Wren said Wednesday his team has moved on. Dempster has the final say because he has 10 years in the big leagues, five with the same team, which allows him to veto any deal.

It's believed Dempster would accept a trade to the Dodgers, who trail the Braves and Pirates by 1 1/2 games in the National League Wild Card standings. Los Angeles GM Ned Colletti has made it clear the Dodgers want to add starting pitching.

Dempster isn't the first to take his time. In 2001, Fred McGriff needed two weeks to decide whether to accept a trade from the Rays to the Cubs.

"This decision gives me an opportunity to control my future," McGriff said at the time. "I had to think about everything as far as, 'Do I want to play?' and 'Where do I want to play?' and 'How long do I want to play?'"

When McGriff finally said "yes" to the Cubs, he received a new contract. Instead of a $6.75 million team option for 2002, which would have become guaranteed with 550 plate appearances, he received a $7.25 million player option, and an $8.5 million mutual option for '03 was added.

"I think time is what finally changed his mind," said Andy MacPhail, then the Cubs' general manager. "It just took him a while to come to grips that this was the best thing for him."

Dempster, 35 and a free-agent-to-be, is also thinking about his future. He has not requested a contract extension as a condition for a trade but did admit that job security is a good thing.

"I think anybody in here is interested in a contract extension," Dempster said. "I think that's true for anybody in whatever job they have. Whatever you're doing, whatever your employment is, I think if somebody wants to offer a contract extension, I think it's something you have to look at."

With Dempster narrowing the list of teams, the Cubs don't appear to have much leverage. They had reportedly sought the Dodgers' top pitching prospect, Zach Lee. However, Dempster would be a two-month rental. It's believed the Dodgers balked at giving up Lee.

Garza is under team control through 2013, and the Cubs may be trying to acquire a package of young talent. The right-hander did come out of his last start after three innings Saturday because of cramping in his right elbow, then returned to Chicago on Tuesday to be with his wife, who was expecting the couple's fourth child. He'll be re-evaluated on Friday.

The past few days, Cubs players have asked reporters for the latest update. Dealing with the rumors has been a "grind," Dempster said. After he was pulled in Wednesday's start against the Pirates, he slammed a water cooler in the dugout, threw the cooler's lid, then a water bottle in frustration. Pittsburgh led, 3-2, Dempster had thrown 93 pitches over six innings and wanted another inning.

"People are competitive," Cubs manager Dale Sveum said, "and sometimes they're going to get upset about things."

Dempster said he wasn't mad at Sveum.

"It seems like so many times I've pitched against these guys and lost by one run," Dempster said. "And I was more upset I gave up the lead and just wanted a chance to get out there and keep pitching and get a chance to win a ballgame. That's all it was."

If Dempster and/or Garza go, the Cubs will have a tough time filling their spots in the rotation. Justin Germano, acquired from the Red Sox on July 19, went three-plus innings against the Cardinals on Saturday. He was a starter at Triple-A Pawtucket and could step in. Chris Volstad and Casey Coleman, both at Triple-A Iowa, would be options. Randy Wells is not after undergoing arthroscopic surgery on his right elbow Tuesday in Chicago.

Dempster planned to use Thursday's off-day to consider his choices.

"The Chicago Cubs are going to do what's best for the Cubs," Dempster said, "and I have a chance to do what's best for me, and I'm going to try to do that."