The Angels, who had previously been viewed as potential frontrunners for free agents Carl Crawford and Rafael Soriano, joined the New York Yankees, Texas Rangers and Washington Nationals as teams known to have an interest in Lee.
The source could not immediately confirm if the Angels have made an offer for Lee. But Angels general manager Tony Reagins said earlier Tuesday he has not made an offer to any free agents yet.
A baseball source said the chances of Lee signing a contract before the end of the winter meetings is "doubtful."
Yankees general manager Brian Cashman is on the verge of making Cliff Lee a very lucrative offer. Cashman is just waiting for the green light from the player's agent.
"I'm willing to get serious," said Cashman, who once again was scheduled to talk with agent Darek Braunecker on Tuesday night.
Cashman said Braunecker is setting the pace of the negotiations so the Yankees must go step for step with him.
The Rangers also continued their pursuit of Lee on Tuesday. Team president Nolan Ryan said that he's more encouraged now than he was a week ago about the prospect of his club landing the pitcher.
"There doesn't seem to be anybody that's stepped out and seems to be the lead pursuer," Ryan said.
Ryan said no offers have been made to Lee and general managing partner Chuck Greenberg added that the talks are still "preliminary." The Rangers met briefly on Tuesday for the second straight day.
Meanwhile, Nationals general manager Mike Rizzo, speaking with Washington-area reporters, downplayed his team's chances of signing Lee.
"I still think we're a real long shot to acquire the player," he said.
Jerry Crasnick is a senior writer for ESPN.com. Information from ESPNNewYork.com's Andrew Marchand, ESPNDallas.com's Richard Durrett, ESPNLosAngeles.com's Mark Saxon and The Associated Press was used in this report.