Neither the Cubs nor the Red Sox have confirmed or commented on the reports. In addition, neither club has formally acknowledged that the Red Sox granted permission to the Cubs to interview Epstein.
WEEI, the flagship station of the Red Sox Radio Network, reported that the deal is worth more than $15 million and that the Cubs had not yet decided on a title for Epstein.
On Tuesday night, Peter Gammons of MLB.com and MLB Network reported that Epstein was weighing an offer from the Cubs. And Boston Herald columnist Steve Buckley reported earlier on Tuesday that Epstein was "on the cusp" of leaving the Red Sox to accept a position with the Cubs that holds powers greater than what he has in Boston.
Gammons reported that Epstein's "friends" in the Red Sox organization believe he is thinking it over, but a club source said, "I don't know which way this is going. There are issues everywhere." Gammons also reported that people in the Red Sox offices, including baseball ops, haven't been told anything.
A source told MLB.com on Tuesday that compensation will be discussed by the two sides only if Epstein decides for sure he wants to go to Chicago.
The Cubs have been looking for a GM since Jim Hendry was dismissed on Aug. 19. He took over in July 2002 and put together teams that reached the postseason in '03, '07 and '08.
Cubs chairman Tom Ricketts has said he wants to hire someone from a winning organization who will emphasize player development while making winning at the big league level a short-term goal.
"I think one thing you've seen in baseball over the last few years is that turnarounds can happen pretty quickly," Ricketts said on the last day of the regular season in San Diego. "I don't think it's meaningful to describe a year as a rebuilding year or a reloading year or any of that.
"The fact is, [if] you get the right players on the team and they all stay healthy and they play hard, a team can go from 70 wins to 90 wins. It happens pretty frequently. Look at the Diamondbacks -- look at the Cubs a few years ago. Things turn around fast, and that's the way we look at things."
The Cubs -- who went 71-91 in 2011 and finished 25 games out of first place -- haven't won the World Series since 1908, the longest drought in professional sports.
Epstein is familiar with overcoming such a drought, having helped the Red Sox win it all in 2004 and '07, the club's first two titles since 1918.
If Epstein does leave for the Friendly Confines of Wrigley Field, it would be the end of a memorable tenure in Boston. Epstein was hired on Nov. 25, 2002, at the time the youngest GM in baseball history at 28 years old.
In Epstein's first season, the Red Sox advanced to Game 7 of the American League Championship Series against the Yankees, holding a three-run lead with five outs to go, only to lose in 11 innings.
But all of the pain from that loss went away in October 2004, when the Red Sox became the first team in history to overcome a 3-0 deficit in a postseason series, defeating the Yankees in a seven-game ALCS and sweeping the Cardinals in the World Series.
Three years later, the Sox again won it all, overcoming a 3-1 deficit to the Indians in the ALCS and this time sweeping the Rockies in the World Series.
In 2008, the Sox were again on the brink of getting to the World Series, only to lose Game 7 of the ALCS to the Rays.
But in the past three years under Epstein, Boston hasn't made a deep October run. The 2009 Sox were swept in the AL Division Series by the Angels.
The past two years, the Sox didn't make the postseason. The 2011 season is one that will live in baseball infamy, as the Red Sox became the first team in history to have a nine-game lead in September and not make the postseason.
The Sox went 7-20 in September, failing to win two games in a row during the month.
Less than 48 hours after the season ended with a walk-off loss in Baltimore, manager Terry Francona and the Red Sox had a mutual parting of the ways.
Now, Epstein might be next. Epstein, who grew up in Brookline, Mass., about two miles from Fenway Park, has come under fire the past couple of years for the lack of success from major free-agent signings.
John Lackey, who signed a five-year, $82.5 million contract with the Sox in December 2009, has struggled mightily since his arrival.
Last December, the Red Sox signed Carl Crawford to a seven-year, $142 million contract, the second largest in team history. Crawford had a near-season-long slump in 2011, hitting .255 with 11 homers, 56 RBIs and a .289 on-base percentage.
When Epstein came to the Red Sox, he proclaimed that the franchise would turn into a scouting and player-development machine.
He backed that up, as Boston produced homegrown stars like Jonathan Papelbon, Dustin Pedroia, Jacoby Ellsbury and Jon Lester over the past decade.
However, Boston's farm system has hit a bit of a lull at the upper levels the past couple of years, and Epstein used three top prospects to land All-Star Adrian Gonzalez from the Padres, a move that has looked good so far.
If Epstein decides to leave, Ben Cherington, his top assistant, could move into the role as general manager. The Red Sox have made it a point to include Cherington in all organizational meetings this winter, including the one in which Francona's fate was decided.
Last week, Red Sox owner John Henry was asked if Epstein was still the right guy for the job in Boston.
"He is," Henry said in an interview with WEEI and NESN. "But I think everyone has to understand a couple of things, and I think [Francona] alluded to it. I think there's a certain shelf life in these jobs [in Boston]. You can only be the general manager if you're sane. You can only be the manager for a certain amount of time. There's a tremendous pressure cooker here.
"There's 162 games. It's a long season, and the pressure here is 365 days. Theo is not going to be the general manager forever. Just as, if Tito had come back for the last two years, would he have gone past 10 years? I can't imagine that he would have. I think that Theo ... he's the guy now, he's been the guy. We've had tremendous success. We fell apart at the end of the season. As [president/CEO] Larry [Lucchino] expressed, we're upset about it. No fan could be more upset than I am about the result this year. He's done a tremendous job for us over the last nine years."
Epstein left the Red Sox on Oct. 31, 2005, resigning from his post when the sides couldn't agree on a new contract. However, he returned two months later.