They said it has been alleged that Busby provided heavily discounted or rent-free housing to selected players at his home and perhaps one other property in Utah County in addition to free meals and other gifts.
ESPN reported Wednesday that BYU is the only school that has won an Associated Press national championship in football and never had a major NCAA violation or received NCAA sanctions. The Cougars won the national title in 1984.
A former BYU player whose last season was in 2012 told The Tribune that Busby's generosity "was something everybody on the team knew about" but that the middle-aged bachelor generally focused on high-profile, offensive skill position players.
"Every year, he had his little buddies that he would kind of pal around with," said the former player, who requested anonymity. "Every year, a handful of guys gravitated to him."
A player who recently completed his eligibility, defensive tackle Eathyn Manumaleuna, said he had no knowledge of allegations that Busby was providing housing or gifts to any players on the 2013 team.
"All I know is he just up and left out of nowhere in March and nobody was told why," Manumaleuna said.
A source said BYU has either self-reported the results of its investigation to the NCAA, or is in the process of doing so. The school will propose self-imposed punishments to the NCAA that could possibly involve the suspensions of current players for one or more games in the upcoming season, the source said.
After receiving an inquiry from The Tribune, NCAA spokeswoman Emily James on Wednesday said via email that the sport's governing body would have no comment regarding an investigation at that level.
"Due to rules put in place by our membership, we cannot comment on current, pending or potential investigations," James noted.
The Zone reported Wednesday that a manager for former BYU receiver Cody Hoffman confirmed that Hoffman was contacted a few months ago by BYU regarding the allegations and that BYU asked Hoffman to come in for an interview. He declined, saying he wanted to focus on his future in the NFL. The manager, Sam Leaf, told the station that Hoffman denied receiving any benefits deemed impermissible by the NCAA.
In an interview replayed on the air, Leaf offered a "no comment" when asked if Hoffman had any knowledge of players who had received improper benefits from Busby.
Several former players who were contacted Wednesday said they did not receive any improper benefits from Busby or anyone else during their tenure at BYU. A few, such as the aforementioned, said it was "common knowledge" that some players received special treatment in regards to cheaper housing, but declined to offer additional details.
When Busby stepped down in March and a school news release said he was "retiring from BYU and college athletics to pursue other interests," Mendenhall expressed disappointment that his staff was losing a key member.
"You don't replace him," Mendenhall said at the time. "He is a personal friend, trusted advisor [and] essential to our success over the last nine years. … Duane is understated, so he asked me specifically not to make a big deal about it. So that's as big [of] a deal as I can make it. But I will miss him."