The university also is investigating if other students are involved. Jenkins said it was too early to say if the four players acted together.
Jenkins said if it is found they violated the school's honor code the penalties could range from an F on an assignment, to an F in the course to dismissal from school. The penalty would be decided by an honor committee.
Swarbrick said the players have not been suspended. He said they remain grant-in-aid students and have access to athletic facilities and resources.
Jenkins said evidence students had submitted papers and homework that had been written for them by others was initially detected at the end of the summer session. The case was then referred to the compliance office on July 29.
Jenkins said he didn't want to speculate on possible NCAA punishment, while Swarbrick said the NCAA usually defers to a university when it comes to academic integrity.
"There are a few narrow instances where that triggers an NCAA concern, but I must stress we have no evidence of most of those here. No involvement by a member of the coaching staff, no transcript impropriety, those sorts of things," he said. "If it has NCAA consequences, we'll let them know."
The investigation is the latest in a series for the Irish in the past 15 months involving academics, starting with Golson.
Jerian Grant, the leading scorer on the basketball team at the time, was suspended in December for the spring semester for an academic violation. Daniels was suspended two weeks later for the spring semester and was recently reinstated.
Swarbrick said the previous cases were different.
"Let's not confuse academic probation where you don't make grades in a semester with academic dishonesty. They are very different things," he said.
Jenkins said he believes it shows Notre Dame's honor system is doing its job.
"At any university you're dealing with young people. The vast majority of them make good decisions. But young people sometimes make bad decisions," he said. "Our job is to hold them accountable and to use those incidents as ways to educate them. That's what we're doing."
Information from ESPN.com's Matt Fortuna, Brett McMurphy and Joe Schad and The Associated Press was used in this report.