Eric W. Orts, along with six other staff members, first called for a probe in July this year after allegations made in a book by the president’s niece, Mary Trump.
Ms Trump claimed that her uncle paid someone else to sit his entrance test to Pennsylvania in 1966, having transferred there from Fordham University, where he studied in the two years previous.
While accepting that the allegations were concerning, University officials decided against a probe, saying that the alleged incident took place too long ago for a meaningful enquiry to take place.
Mary Trump said she recorded conversations with the president’s sister, Maryanne Trump Barry, which backed up the claim that he cheated the test.
At the weekend, The Washington Post published audio of that recording, which Prof Orts says constitutes “new evidence”, worthy of an investigation.
Mary Trump said it was a man named Joe Shapiro, a student at Pennsylvania, who took the president’s test.
The White House has has dismissed the audio recordings of Maryanne Trump Barry, branding them “sibling rivlarly”.
According to Mr Trump’s former fixer, the disgraced lawyer Michael Cohen, the president ordered him to “to threaten his high school, his colleges and the College Board to never release his grades or SAT scores”.
Mr Trump has frequently boasted that he was a stellar student, but he declined throughout the 2016 campaign to release any of his academic records, telling The Washington Post then: “I’m not letting you look at anything”.
In 2018 Mr Trump suggested he was “first in my class” at the University of Pennsylvania’s Wharton business program, where he finished his undergraduate degree.
But his name does not appear on the school’s dean’s list or on the list of students who received academic honours in his class of 1968.
The Independent has contacted the White House for comment