Connors, whose name has already been highlighted as a likely bidder for the Globe, and Stephen Pagliuca are leading one group.
Connors is now chairman of Partners HealthCare and a prominent Boston business figure while Pagliuca is the co-owner of Boston Celtics and a Bain Capital executive.
The other group is being led by Stephen Taylor, a former Globe executive and member of the family that sold the paper to the New York Times Co in 1993 for $1.1bn.
According to a report in the Boston Globe, interested bidders had until yesterday to submit their plans for the paper and its website.
The Connors-Pagliuca group is understood to have proposed a non-profit foundation to run the paper -- a business model that would make enough money to run the paper without the onus of generating large profits.
The New York Times Co is expected to examine the bids before deciding who to invite to the next round in the auction. At that stage, bidders will be expected to submit more detailed proposals, while the seller would be obliged to provide potential buyers with more information.
The Globe said that is was unclear whether other parties who had previously expressed an interest in the paper had submitted bids.
One of those parties is Mortimer Zuckermann, a billionaire real estate investor who had requested the sale-offering documents from Goldman Sachs, the New York Times Co's bank.
The media group, which has forecast a $85m loss for the Boston Globe this year, has also asked that potential new owners take on the paper's $51m pension liabilities and $8m for sister paper the Worcester Telegram & Gazette, which it wants to package with the Globe.
However, according to Globe sources, there is a possibility that the latter could be sold separately.
Connors, Pagliuca and Taylor's names became linked to the auction in June.
Connors sold what was Hill, Holliday, Connors, Cosmopulos in 1998 to the Interpublic Group for more than $115m.
At the end of 2006, when he last tried to buy the Boston Globe, he told a reporter about his plans to improve the paper.
He said at the time: "Could it be better? It was better. Circulation is down, so they cut back on the product.
"I have a counterintuitive notion. You invest in the product. You make the product better. I think it is disappointing that the Globe has been forced to cut back, cut back, cut back. That is not how you build. I didn't build things by cutting back."
His acquisition attempt floundered because the New York Times Co said is did not want to sell.