Queen's University has said it is reviewing "the nature of its relationship" with the Presbyterian-run Union Theological College, which teaches its degree courses in theology.
he Belfast Telegraph understands that a factor in the decision is the suspension of Professor of Church History Laurence Kirkpatrick. He is believed to have been suspended from his college role due to comments he made in the media.
Last week clerk of the Assembly Rev Trevor Gribben issued a letter to all Presbyterian ministers warning against bringing the Church "into disrepute" by speaking in public in a way that may cause "scandal injurious to the purity or peace of the Church".
It followed a decision by the General Assembly not to allow anyone in a same-sex relationship to be a full member of the Church or have their children baptised.
Professor Kirkpatrick had described the college as a "'getting on' exclusively Presbyterian male teaching faculty" on Radio Ulster's Talkback earlier this month.
He added: "I'd be broken-hearted if anyone said I'd been bigoted against a Catholic or gay student."
He also told BBC's The View that the Church could be extinct by 2073 if membership continued to dwindle at its current rate.
Former Presbyterian minister Rick Hill said he believed Prof Kirkpatrick's suspension was "just the beginning" of what "might be a censorship policy".
"It's very disappointing to see Prof Kirkpatrick's academic freedom curtailed," he said.
"It undermines academics, who have always had the ability to express a range of opinions.
"It's disgraceful. They shouldn't be stifling public debate, and this is a matter of public interest. I think Queen's University should review the arrangement with the college.
"Mr Gribben's letter lends itself to the interpretation that there might be a censorship policy."
Mr Hill said he had been contacted by "many people" "astounded" at Prof Kirkpatrick's suspension but who were afraid to speak out.
"Clergy have talked to me and said they can't express a view or they would be summoned to a disciplinary panel," he said.
Former Alliance leader David Ford, a Presbyterian Church elder, said he "couldn't see why" Prof Fitzpatrick had been suspended.
"It appears consistent with the warning issued by the clerk of the General Assembly, but I cannot see how open and honest discussion brings anybody into disrepute," he said.
"It appears to me that there are questions about the whole handling of the issue which do not appear to link into the liberty of conscience which is the stated position of the Church."
Queen's University said: "In light of a number of developments in recent weeks, the university is taking active steps to review the nature of its relationship with Union Theological College and several options are currently under consideration."
The Presbyterian Church said: "As an employer we don't comment on any such matters and even if there was an employment matter under consideration, like all other employers, it would be inappropriate to make any comment publicly."