Speaking to the Ciara Phelan Podcast on the Irish Examiner, Fr. McVerry said he would have left the priesthood years ago if his understanding of God had not changed.
He told Phelan that he would prefer people to replace the word God with a different word.
"I’d prefer to use the word mystery. We live within a mystery. I think people can understand that," Fr. McVerry told Phelan.
"One of the things we all search for is meaning - what's the meaning of life? And that can be found only in mystery.
"We keep searching to understand who God is. We'll never understand who God is because God is mystery."
Fr. McVerry also discussed celibacy in the Catholic Church during the interview and said he would not have been able to do the work he has done with homeless communities if he had a "family and children to look after".
However, he also admitted that it is difficult to persuade young people to join the priesthood due to the discipline that requires priests to abstain from sex.
Fr. McVerry said it is difficult to convince young people to take a vow of celibacy in a highly sexualized world where "sex is in front of your eyes everywhere".
He also believes that young people are sexualized too young due to their access to digital devices.
"Celibacy is a huge ask for young people in today's world."
Fr. McVerry added that he is in favor of women joining the priesthood and said he believes the church should be run by lay people in the future, shifting away from a focus on the priesthood.
"For me, it's not a question of priests. We shouldn't focus on priests. The church of the future is going to be run by laypeople. If priests have a role, it will be as a leader of the community and as a minister of the sacraments."
Fr. McVerry described himself as a " very angry" man during the 45-minute interview, criticizing the way homeless people, vulnerable people, and people on the margins are treated by the authorities in Ireland.
"I think my anger has grown and become more focused over the years. There should be no homelessness in a country as wealthy as Ireland. There should be no poverty in a country with billions of euros in surplus taxation.
"There should be no children on long waiting lists for mental health
treatment," he added. "I just think we have our priorities all wrong."