Epstein, the Cubs' president of baseball operations, met the combustible pitcher for lunch at a restaurant near Wrigley Field on Monday to get to know each other. Zambrano requested the meeting, according to his agent, Barry Praver, who also attended the lunch, as did Oneri Fleita, vice president of player personnel for Chicago.
"It went well," Epstein said. "[Zambrano] expressed a strong desire to be a Cub and an even stronger desire to have a really good 2012 season."
Zambrano has made two starts this offseason, including a six-inning outing on Saturday, for Caribes in the Venezuelan Winter League. He flew to Chicago on Sunday and will return to Venezuela on Tuesday.
"I told him we'd give him the right to earn his way back to being a Cub," Epstein said. "Nothing would be given to him, but he could earn his way back from very hard work this winter, through rebuilding relationships man to man with all of his teammates, and through some other steps that we discussed.
"We're not welcoming him back unconditionally at all, but we're going to give him the right to earn his way back to being a Cub."
Neither Epstein nor Praver would go into detail as to what those steps will be.
Zambrano last pitched for the Cubs on Aug. 12 against the Braves. In that game, Zambrano served up five home runs, then was ejected for throwing inside at Chipper Jones. Zambrano left the ballpark, telling teammates he was retiring.
Zambrano was placed on the 30-day restricted list and did not rejoin Chicago, finishing 9-7 with a 4.82 ERA. He is under contract for next season and has a full no-trade clause.
In September, Cubs chairman Tom Ricketts said he had a hard time imagining Zambrano returning to the team. The right-hander has tested the club's patience with his behavior, which prompted the team to order him to undergo anger-management therapy in 2010.
"There are steps," Epstein said of what Zambrano must do. "Most of the details will stay confidential. There are steps he needs to take and he seems motivated to do so, and if he earns his way back under certain conditions, we'll see him in Spring Training and welcome him back."
Was Zambrano contrite during their meeting?
"Yeah, very much so," Epstein said. "But from what I understand, he's been that way before."
Praver said it was a good meeting, but would not go into details. Asked if he thought Zambrano would be pitching for the Cubs in 2012, Praver said, "I'd rather not get into details on my personal feelings about it."
Carrie Muskat is a reporter for MLB.com. She writes a blog, Muskat Ramblings, and you can follow her on Twitter@CarrieMuskat. This story was not subject to the approval of Major League Baseball or its clubs.