This is not your grandmother’s Catholic Church.

Archbishop Pietro Parolin, the new Vatican secretary of state, said Catholic leaders are open to discussion about one of the church’s touchiest issues — celibacy for priests — on grounds that it’s not formal church dogma and therefore could be changed.

“Celibacy is not an institution, but look, it is also true that you can discuss [it] because as you say this is not a dogma, a dogma of the church,” Parolin told Venezuela’s El Universal newspaper.

Parolin said the church needs to “reflect the democratic spirit of the times and adopt a collegial way of governing” the flock.

“It is possible to discuss and reflect on these topics that are not defined faith, and consider some modifications, but always in the service of unity and according to God’s will,” Parolin added.

Parolin was appointed secretary of state last month by Pope Francis to replace Tarcisio Cardinal Bertone, who quit after being blamed for failing to prevent the financial and ethical scandals that rocked the reign of Pope Benedict XVI.

The Vatican’s secretary of state — the second most powerful position within the Holy See — acts as the pope’s prime minister and chief aide, but has no power to act on doctrinal issues.

It is not clear exactly when Rome ordered celibacy for priests.

The first written mandate for chastity dates back to the year 304, when the Council of Elvira stated that all “bishops, presbyters, and deacons and all other clerics” should “abstain completely from their wives and not to have children.”

A more formal ruling was handed down at the Second Lateran Council of 1139, which said priests were forbidden to marry.

Pope Francis hasn’t addressed the subject of priestly celibacy since succeeding Benedict, who resigned in February.

But Francis discussed the issue — seen as a major reason for the worldwide shortage of priests — when he was still Jorge Cardinal Bergoglio, archbishop of Buenos Aires.

“It is a matter of discipline, not of faith. It can change,” he said in 2012.

During that interview, he also confessed that while a seminarian, he was tempted by a woman he met at an uncle’s wedding.

“I was surprised by her beauty, her intellectual brilliance . . . and, well, I was bowled over for quite a while,” he said.