Gloria Trevisan, 27, and Marco Gottardi, 28, arrived in London around three months ago and were living on the 23rd floor of the building.
The engaged couple are architects from the Veneto region, and are the only Italians missing following the fire.
A lawyer representing Trevisan’s family said they were hoping for the best but bracing for the worst.
"I heard the recording of Gloria's phone call to her mum," lawyer Maria Cristina Sandrin said.
"She says thanks for what she did for her. They were saying goodbye. There are no grounds to hope that Gloria and Marco are still alive."
Gottardi's father Giannino said he had been on the phone to his son up until the final moment, when smoke had already inundated the building.
“Marco was extraordinary and calmed everyone else down,” he said.
“When the line was cut, we understood that the situation had grown worse and we became desperate. I will always remember the last words he said to us."
The suffering father added that he refuses to lose hope for his son until the couple’s fate is confirmed.
“As the hours pass, we are losing the slim hope we still have,” he said.
“But until they tell us they have found our children, we will continue to believe in a miracle."
Officials in London said on Thursday that they do not expect to find any survivors inside the Grenfell Tower.
At least 17 people have died in the inferno which occurred in the early hours of Wednesday morning.
With ANSA
