But there is no bell in the tower, the school said.
According to USA media reports, Ms Monfries slipped on her way up the tower's spiral staircase and was found by emergency services at about 3.17am.
Monfries, a journalism student, had been set to graduate in May and was allegedly participating in a rite of passage many Fordham University students undertake prior to graduating when she fell on Sunday morning. "I think they were posting on Instagram when it happened".
In a statement, Fordham University said they student's family has been notified, and university officials are investigating how the students gained access to the tower, which is supposed to be locked and off limits.
The university said authorized school officials "have sometimes given tours of the tower, in part to satisfy students' curiosity about it, and reduce the likelihood that they would attempt to enter the structure without authorization".
"I heard they were just getting a better view of the city", she said.
Police said Monfries and her friends snuck into the Keating Clock Tower around 3 a.m. Sunday and were going to try to climb to the top.
Access to the tower is restricted, a university spokeswoman told the Times. She fell 40 feet through the inside of the tower and struck her head on the ground.
"She was with a group of friends ..." However, a senior, Anne, who declined to give her last name, said that "the doors aren't always locked". They're unlocked at night when they're cleaning.
The budding journalist, who was due to graduate next month, had completed a string of internships at a news network, InStyle magazine and a public relations company.
School president Joseph McShane confirmed the tragic news in a letter to students later that evening. She was rushed to St Barnabas Hospital in "extremely critical condition" where she later died.