The source also told ESPNChicago.com's Bruce Levine that Haren is just one of many starters the Cubs are considering.
The Boston Red Sox are one of several teams, a baseball source told ESPNBoston.com's Gordon Edes, that have talked to the Angels about Haren, who told ESPNLosAngeles.com on Thursday that he hasn't heard much from the Angels of late but believes "a trade is the likeliest scenario" now that his no-trade clause is invalid after the World Series ended.
Boston's chances of making a deal did not look strong Thursday night, the source said, as the Angels must decide by midnight ET Friday whether to exercise the $15.5 million option on Haren's contract, and if they do, whether to keep him or trade him. They can buy out his option for $3.5 million, which would make him a free agent.
It is possible that the Angels could pick up the option and then trade Haren, just as they did earlier this week with another of their starters, Ervin Santana.
The Angels picked up Santana's $13 million option and then dealt him to the Kansas City Royals for minor league left-hander Brandon Sisk. The Angels also sent cash to the Royals, but Kansas City is reportedly picking up the majority of what Santana will make next season.
Haren would likely be just a one-year rental for the Cubs, but the chance to add a quality starter without going through the free-agent process has some intrigue for the club.
"I'm not going to characterize those particular negotiations, but certainly it's an interesting twist," general manager Jed Hoyer said. "You have a couple of guys who theoretically could have their options exercised like they did with Santana and then traded right away. In some ways, Kansas City avoided free agency. It's interesting."
The question would be what the Cubs would have to give the Angels in return for Haren. Sisk, who was acquired for Santana, was not among Baseball America's top 10 prospects before the 2012 season, but Haren figures to yield more of a return for the Angels.
Haren had a down 2012 season by his standards -- a 12-13 record with a 4.33 ERA. He was bothered by back issues.
"I loved my time with the Angels," Haren told ESPNLosAngeles.com via email. "I would come back if we worked out something fair for both sides, but I'm not getting a feeling from them that the feeling is mutual."
The Cubs' best chance of landing Haren would be via trade. If he becomes a free agent, the Cubs would probably be a long shot to sign the Southern California native.
Information from Ramona Shelburne of ESPNLosAngeles.com was used in this report.