The Sox have been seeking left-handed power in their stretch run for the playoffs, and the 38-year-old Delgado has 473 home runs and 1,512 RBIs. Chicago has been in pursuit of a left-handed hitter since letting Jim Thome leave as a free agent in 2009.
"We've been talking to a handful of teams who have interest in Carlos," said David Sloane, Delgado's agent. "I epxect that he will be signed by as early as next week."
The White Sox had scouts look at Delgado during winter ball in Puerto Rico, but they decided at that time he wasn't completely back from hip surgery. He hasn't played since May, 2009.
Sloane said Delgado had a private workout for a handful of teams.
"He's going to need a minor league rehab assignment," Sloane said. "He has been working out, but he needs to get his timing down and only live pitching can solve that."
If the White Sox sign Delgado, he ultimately would be used as their primary left-handed designated hitter.
"I thought this guy was building houses in Puerto Rico," White Sox manager Ozzie Guillen said Thursday. "[GM Ken Williams] hasn't talked to me about it.
"If they did it, he has to go to the minor leagues first. He hasn't played in a couple of years. He has to prove people he still can play and is healthy. Maybe he can help. I don't expect anything to help me right now."
Delgado is a below-average runner and well-below average defensive first baseman. His limited range has been exacerbated by hip surgery.
Sloane said not all the interested teams are contenders.
"No, at least one of the teams is not a contender, but it could be a nice situation where he gets a lot of at-bats and a leg up going to next year," Sloane said.
Bruce Levine covers baseball for ESPNChicago.com. ESPNChicago.com White Sox beat writer Doug Padilla contributed to this report.