The person spoke on condition of anonymity because the conference did not plan to make any announcements.
Commissioner John Marinatto has a teleconference scheduled with reporters for Tuesday.
The Big East is hoping the move will lead to adding six new schools to the conference, including Boise State as a football-only member.
The exit fee will remain $5 million for the league's eight non-football members, the person said. The results of the vote were first reported by CBSSports.com.
The Big East's plan to have 12 football members also includes adding Navy and Air Force just for football and Conference USA members Central Florida, SMU and Houston in all sports.
There is no timetable for extending invitations and no guarantee all the targeted schools will join. But upping the exit fee is a way to signal to potential new members the Big East will be stable long term.
The question is: Will that be enough to convince Boise State and Air Force to leave the Mountain West Conference, and Navy to give up football independence?
Officials from all those schools have expressed concerns about the stability of the Big East.
What the Big East does have going for it -- at least for now -- is an automatic bid to the Bowl Championship Series. The MWC and CUSA do not. Those two leagues announced last week they will merge for football by 2013, if not sooner, with the hope of increasing the chances to receive an automatic bid from the BCS down the road.
The Big East made Boise State a priority in expansion, along with Air Force and Navy, to help ensure the league keeps its automatic bid to the BCS beyond 2013.
"I've been very vocal about my thoughts regarding the BCS and when they organize in 2013, I hope there's a way to deal with some of these inequities," Boise State President Bob Kustra told the AP on Saturday. "But in the meantime, it seems like our responsibility is to get as close as we can to AQ status as we can."
Boise State is nearly 1,900 miles away from the Big East's closest current member, Louisville, but with Air Force, based in Colorado Springs, and the two Texas schools the league can create a western division.
The Big East is on shaky ground, trying to reconfigure after losing two members, and one would-be member, in the last two months. Pittsburgh and Syracuse announced last month they will move to the Atlantic Coast Conference. Big East rules require them to stay in the league for the next two seasons and Marinatto has said he will hold the Panthers and Orange to that. It seems unlikely Pitt and Syracuse will be forced to stay if the Big East can get to 12 football members by 2012.
TCU was slated to join the Big East in 2012, but the Horned Frogs reneged on that commitment and accepted an invitation to the Big 12. TCU is free to go immediately because it was never an official member, but the Big East is expecting to collect a $5 million exit fee.
Trying to recruit new members has been tricky for the Big East because its remaining members have not committed to stay in the league.
Louisville and West Virginia are possible targets for the Big 12 if it needs to replace Missouri -- which is pondering a move to the Southeastern Conference -- or if it decides to expand back to 12 teams.
Connecticut has interest in joining the ACC if it expands again, and there has been speculation about Rutgers moving, too.
The Big East also has eight members that do not compete in the league in football: Villanova, Georgetown, St. John's, Providence, Seton Hall, Marquette, DePaul and Notre Dame.