The couple has been named in Italian media as Gloria Trevisan and Marco Gottardi, both aged 27 and from the Veneto region. Italy's Foreign Ministry said that two Italians are among the missing, but has not yet confirmed their identity.
Gottardi's father said he had been speaking on the phone to his son “up until the last minute”.
“They told us that the flat was full of smoke, then the communications were interrupted,” he told news agency Ansa. “We're just hoping for a miracle.”
The last phone call took place shortly after 4am. Gottardi's father said his son had initially played down the extent of the fire in order to reassure his girlfriend and family members, and labelled his behaviour “heroic”.
Trevisan and Gottardi had both graduated in architecture and travelled to London to work and improve their English skills, Italian media reported.
They had lived on the 23rd floor of Grenfell Tower, and Trevisan had posted a photo of the view from their apartment on Instagram just a few days before the disaster, accompanied by the caption: “What a beautiful view.”
London police have confirmed that at least 12 people died in the fire, and said that number was “expected to rise”.
Firefighters were on Thursday morning continuing their search of the building and had reached all 24 floors, but said it was not safe to go into some parts of the upper floors, where there were still pockets of fire.