A person with knowledge of the plans told The Associated Press that the board's meeting is expected be followed by a "major announcement." The person spoke on condition of anonymity late Sunday night because the university was not ready to publicly reveal its plans.
The Big 12 issued a public invitation to TCU for membership in its league Thursday.
With Texas A&M's pending departure to the SEC next summer, the Big 12 would be down to nine members without TCU's addition. Missouri is also considering its conference options after Nebraska and Colorado left the league this year.
Monday's session will be the first time TCU's board of trustees will gather as a group since the Big 12's invitation.
Though TCU has not officially accepted the Big 12 invite, that has been expected to be little more than a formality since last week.
While TCU isn't required to give 27 months' notice to leave the Big East since it is not an official conference member, the school likely will be required to pay a $5 million exit fee.
Syracuse and Pittsburgh already have announced they are leaving the Big East for the Atlantic Coast Conference.
With those departures and without TCU, the Big East would be down to six football schools.
TCU would be the first addition to the Big 12 since the league started play in 1996 after all eight members of the Big Eight Conference and four Southwest Conference schools from Texas combined.
A conference-hopping journey followed for the Horned Frogs after they were snubbed for the original Big 12.
The Frogs first went to the Western Athletic Conference, then to Conference USA and the Mountain West. They won or shared football titles in each of those leagues and became a two-time BCS buster.
TCU last season finished No. 2 in the final AP poll after a 13-0 season they capped with a win over Wisconsin in the Rose Bowl. Their only loss during a 12-1 season in 2009 was to Boise State in the Fiesta Bowl.
When TCU announced 13½ months ago its intention to join the Big East, school officials touted joining a league with an automatic Bowl Championship Series slots.
After the Big 12's invitation last week, TCU Chancellor Victor Boschini Jr. released a statement suggesting the school's desire to be part of the league closer to home.
"These discussions with the Big 12 have huge implications for TCU," Boschini said then. "It will allow us to return to old rivalries, something our fans and others have been advocating for years."
Although TCU would not expand the league's television footprint, the Horned Frogs would add a Big 12 member in the Dallas-Fort Worth area. It would join Baylor as the league's only private schools.
TCU's football stadium is undergoing a $143 million modernizing renovation scheduled to be completed by the 2012 opener.