Dempster will consider a number of teams, including the Atlanta Braves and Dodgers, if the Cubs come to him with a deal in place, the source said.
"He has not said that he wouldn't go to Atlanta or anywhere else for that matter," the source said. "He wants to take his time and has earned the right to wait on approving a deal having his 10-5 rights."
Reports surfaced Monday that the Cubs and Braves agreed to a trade of Dempster for 22-year-old pitcher Randall Delgado, pending the approval of the Cubs pitcher, who has veto power on any trade. Dempster said he wanted to take his time before making a decision on any trade.
But Braves general manager Frank Wren told an Atlanta radio station on Wednesday that they are "moving on" from a Dempster deal, and he said Dempster wants to land with the Dodgers and his good friend and former Cubs teammate Ted Lilly.
"In his case, from my understanding, and I'm only getting it secondhand from the Cubs, they had a meeting with him a couple of weeks ago and laid it out and that the primary two suitors were us and the Dodgers," Wren said on 680-AM The Fan. "He had positive things to say about both, but he had a slight preference to the Dodgers because of Ted Lilly. He and Ted Lilly are best of friends, and he'd like to go play with his friend. I think there were also some personal issues that suited better for him."
A trade with the Braves still could resurface if Dempster chooses to waive his veto rights and accept a deal; however, Atlanta took its deal off the table on Tuesday.
The Toronto Blue Jays, New York Yankees, Dodgers and Braves were on Dempster's original list for consideration, according to another source. The Washington Nationals have also shown some interest but have not made an offer for Dempster. Washington will sit down young ace Stephen Strasburg at some point around his160-inning mark and will need a veteran starter to plug in for him.
The Dodgers have had an offer on the table since July 19 for Dempster. The Cubs would like the Dodgers' top prospect, right-handed pitcher Zach Lee, added in the deal, according to sources. That may have caused a stalemate between the two sides. The Cubs continue to seek young pitching and third-base prospects in talks with other teams.
Dempster is owed a pro-rated amount, close to $5 million, of the $14 million he is making in the final year of his contract.