School spokesman Bob Howe told the New York Post the tower was "always locked" and that the organisation was looking into whether the lock had been tampered with.
"Access to that tower is always locked," he said. "University officials are investigating how the students gained access to the tower."
However, Anne said the Keating Hall clock tower was regularly left open at night.
"The doors aren't always locked. They're unlocked at night when they're cleaning. They are always doing some kind of cleaning or renovation," she said.
The Sun reported another student, only identified by the first name Dave, claimed Ms Monfries and her friends had dined at a restaurant where he worked shortly before the accident.
"She was with a group of friends … They were like, 'We're seniors, let's go!'" he said.
"My roommate was with them. He told me some seniors (wanted to go) to the tower to take some pictures and have a good time before graduating."
The waiter, whose roommate allegedly arrived on the scene shortly after the fall, said she was gravely injured.
"She couldn't breathe. She hit her head. If he wasn't there, I don't know, she might have been worse off," he said.
He said Ms Monfries and her friends left the establishment an hour or two before it closed at 4am.
According to US media reports, Ms Monfries slipped on her way up the tower's spiral staircase and was found by emergency services at about 3.17am.
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.
University president Joseph M McShane told NBC New York Ms Monfries would be awarded her degree posthumously.
"There are no words sufficient to describe the loss of someone so young and full of promise — and mere weeks from graduation," he told the network.
US media reported emergency services struggled to rescue gravely injured Ms Monfries from the building after they realised it wasn't possible to carry her via stretcher down the staircase.
Instead, she was strapped into a rescue basket which was lifted out of a window before being lowered to the ground.
During the painstaking process, a paramedic performed chest compressions on the young woman whose heart rate had dropped.
Ms Monfries' family rushed to her hospital bed and were accompanied by two priests, the Post reported.
Her death was announced to students in an email sent by the school, which described the "unimaginable loss" suffered by Ms Monfries' family, friends and school community.
According to the university's website, Fordham University is a Jesuit, Catholic institution focused on instilling students with "wisdom, experience, morality, critical thinking and creative problem-solving".
