The board is scheduled to meet at 9:30 a.m. Saturday at the Epley Board Room in the Arkansas Union. There is no mention of Broyles' resignation on the agenda, but there is a provision for an executive session, as is routine for all board meetings.
If Broyles, 82, does make an announcement, it will be "positive," a source close to the situation said Thursday.
That could mean Broyles will continue with the school in some capacity and possibly stay on as athletic director until the end of the year. Broyles would complete his 50th year at the university in December.
"Dad has been considering retiring for two or three years," a Broyles family member said Thursday. "But he just loves the University of Arkansas, and has for 50 years.
"He's newly married, healthy and very happy. But if he retires, I think he'll do something else part-time. He believes it's important to stay mentally active."
Broyles was in Chicago on Thursday, visiting a friend in the hospital, according to family members. He was unavailable for comment.
Max Brantley of the Arkansas Times, a weekly newspaper in Little Rock, reported on his Web blog Thursday that Broyles was given an ultimatum to step down or be fired. Other news sources across the state were also reporting the move Thursday evening.
However, a source told The Morning News that even if Broyles did not resign Saturday that "he would not be fired."
Tim Hunt, a Paragould native who serves on Arkansas' Board of Trustees, said Thursday he didn't want to elaborate on whether Broyles was pressured to retire.
"If we were to be discussing that -- and I'm not saying we are or not -- that would be a personal matter and I would not be able to comment to you publicly," Hunt said.
Charles Scharlau III, another UA Board of Trustees member, didn't want to comment about the situation.
"I didn't see anything on the agenda like that," Scharlau said.
There have been indications for several weeks that Broyles was contemplating retirement.
"Dad will do what's best for him and the university. He's always put the university first," another Broyles family member said. "He's wondered, will he live longer being the athletic director or not being the AD. He makes that choice every day -- every minute, I'm pretty sure."
Broyles' retirement could lead to sweeping changes within Arkansas' athletic department. Northwest Arkansas NBC affiliate KNWA reported Thursday night Arkansas football coach Houston Nutt's contract could be bought out sometime in the next three weeks.
When reached Thursday night and asked about the report, Nutt had no comment.
Broyles has been the athletic director at Arkansas for the past 33 years after a long and successful career as the head football coach, where he compiled a 144-58-5 record in 19 seasons. The Razorbacks captured the 1964 national championship, seven Southwest Conference championships and made 10 bowl game appearances.
As the athletic director, Broyles has been credited with building solid sports programs across the board, including the nation's most successful men's track and field program with 42 national titles. In all sports, Arkansas has won more than 100 Southwest and Southeastern conference titles under Broyles' leadership.
Among the honors Broyles has accumulated are induction into the National Football Foundation and the College Football Hall of Fame in 1983, induction into the Orange Bowl, Cotton Bowl, and Gator Bowl halls of fame, induction into the Arkansas, Georgia and Georgia Tech halls of fame and a Fellowship of Christian Athletes Lifetime Trustee.
His most notable accomplishments as athletic director are taking Arkansas from the Southwest Conference into the Southeastern Conference in 1992, and the $230 million in facilities improvements, including the expansion of Reynolds Razorback Stadium in 2001.
THE MORNING NEWS' ALEX ABRAMS AND HARRY KING CONTRIBUTED TO THIS REPORT.