The next "Holy War" game is billed for 2015, with Notre Dame athletic director Jack Swarbrick set to unveil the 2014-16 schedules Friday morning.
The talks between the schools and the Fenway Sports Group have been ongoing for a few years, The Globe reported. Boston Red Sox chief operating officer Sam Kennedy declined comment on the possibility of a forthcoming agreement.
This would be the first major college football game at the legendary ballpark, according to The Globe. The home of the Red Sox has also hosted New England Patriots games, the NHL's Winter Classic and college hockey -- Boston College played Boston University in the Frozen Fenway game in January 2010.
Notre Dame leads Boston College 13-9 in their football series, which dates to 1975.
ESPN.com's Matt Fortuna contributed to this report.