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 results of the vote were first reported by CBSSports.com.
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 the league will be stable long term.
The question is: Will that be enough to convince Boise State, Navy and Air Force, all of which have expressed concerns about the stability of the conference, to come aboard?
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.