The couple are believed to live in England.
The investigation began after the Colosseum Park Authority was alerted to the incident by a video, allegedly filmed of the pair and posted on social media.
The English-speaking tourist was filmed by an onlooker using keys to engrave “Ivan+Hayley 23” into the wall of the 2000-year-old Roman amphitheatre.
Earlier this week investigators said the young tourist risks at least a €15,000 fine and up to five years in jail for the act of vandalism.
“I am grateful to the Carabinieri for having promptly identified the alleged perpetrator of the uncivilised and absurd act committed at the Colosseum,” Culture Minister Gennaro Sangiuliano said.
“(It is) an act that offended all around the world who appreciate the value of archaeology, monuments and history.
“I now hope that justice will take its course by strictly applying the laws.
“If the case goes to trial, the Ministry of Culture will be a civil plaintiff,” he added.
Earlier this week Tourism Minister Daniela Santanchè called for Italy’s culture and history to be respected.
“We cannot allow those who visit our nation to feel free to behave in this way,” she said.
While not a regular occurrence, this is not the first time in recent years that the Colosseum has been defaced.
In September and October of 2020, in separate incidents, a 32-year-old Irish national and a 14-year-old German girl both used metal points to carve their initials into the ancient monument.
Commenting on The Guardian news website, the director of the Colosseum, Alfonsina Russo, said there appeared to be a “lack of education” among people who commit such acts.
“Anyone who writes on monuments has obviously not been educated about our cultural heritage,” she said.
ANSA