The owners of the Boston Red Sox are mulling a potential sale of the storied baseball franchise, and have even begun quietly shopping the team to potential buyers, the FOX Business Network has learned.

The team is owned by the Fenway Sports Group, which also owns the English football team Liverpool FC. While no final decision has been made about a potential sale, and the talks appear to be in the early stages, executives at Fenway Sports are debating whether they have the financial resources to run both teams, according to people with direct knowledge of the matter.

The Red Sox have publicly denied that they are for sale. Reached Thursday, a spokesperson for the team said of the potential sale that “there is no truth to that rumor.” However, there has been talk for some time that the team is informally gauging interest in the club.

The price tag eyed for any potential sale would be a steep one, according to people who have spoke with Red Sox management: $1.3 billion. Forbes cites the value of the Red Sox at around $1 billion.

Financier John Henry is the principle owner of Fenway Sports, which bought the Red Sox in 2002 and produced immediate results, winning the World Series in 2004 and 2007. But the last two seasons have been dismal ones for the team, plagued by injuries and overpaid talent.

Recently, the team unloaded a slew of underperforming players, saving as much as $250 million through 2018.

Also likely weighing on the consideration to sell the team is the poor performance of Henry’s investment company, John Henry & Co. this year, these people say. The firm, which specializes in the futures market, has had a volatile year, with funds such as his Global Analytics losing nearly 16% this year, according to the company’s website.

But according to people with direct knowledge of the matter, the biggest challenge for Henry is running two expensive sports franchises. Fenway Sports purchased the Liverpool team for $476 million in 2010, and has been widely criticized for overpaying for players who have under-delivered.

In fact, Henry recently wrote an open letter to Liverpool fans, vowing not to overspend on talent in the future, but stating his commitment to keeping the team.

By weighing a sale of the Red Sox, Henry could devote more resources to the Liverpool team. Also, unloading Liverpool is considered more difficult compared with a franchise with the name recognition of the Red Sox, despite its lousy 2012 season.

Fenway also owns 80% of the New England Sports Network, where the Red Sox games are aired, as well as the Boston Bruins of the National Hockey League. It's unclear how the sports network would factor into any deal.

In fact, people close to executives inside Fenway say management has been increasingly focused not on the Red Sox, but on the future of the Liverpool team.

If NESN was included in a full auction of the Red Sox, the ball club could fetch $1.5 billion to $1.6 billion, said one person intimately involved in financing sports deals. 

"The Red Sox are one of the premier franchises in all of sports. I don’t think it would be very hard to sell the team. You would have many, many bidders," the source said.

In addition to saving on payroll, the fire sale of Red Sox talent earlier this season also makes the franchise a "more attractive asset," allowing a new owner to "recast the team the way he wants," the source said. 

Matt Egan contributed to this story. 

Charles Gasparino joined FOX Business Network (FBN) in February 2010 as Senior Correspondent.