Formal identification is yet to take place, but Police Scotland say relatives have been informed. A 21-year-old man has been arrested.
"It's the worst news that parents could hope to meet. It must be dreadful for them. I suppose at least, they're given a chance to have some idea as of things have finalised," said Revd Canon Gerard Casey, parish priest of Mallow, near Mourneabbey, County Cork in the Republic of Ireland where Karen Buckley's family live.
"To think that she could be suffering somewhere would be perhaps more difficult. God spare them and protect them and help them. There was a mass of hope that took place last night and there was an enormous crowd from all over north Cork in support of the family.
"It will help them to know that that support was there I think, but at this stage we must only pray for them, that God would help them to cope with what they have on their hands," added Revd Casey.
Karen Buckley, 24, who was studying Occupational Therapy at Glasgow Caledonian University, went missing on Sunday after a night out in Glasgow.
Police have previously said a man told them she left the Sanctuary nightclub with him and went back to his flat. This man also said she left his flat at approximately 4am to go home, a journey of around four miles.
Detectives then found a handbag Dawsholm Park in the northeast of the city which they believe is Miss Buckley's, before investigations led them to a farm near Milngavie, north Glasgow.
It was at this farm that police found human remains, believed to be of Karen Buckley.
Listen to Very Rev Canon Gerard Casey speaking to Premier's Aaron James: