Having only left Inter to join Chelsea in a reported £97.5 million ($170 million) deal last August, Lukaku is reportedly keen to move back to the club where he won the Serie A title last year.
Inter's managing director Alessandro Antonello said earlier this week that the forward holds a "great desire" to return after scoring just eight Premier League goals during an underwhelming 2021-2022 season at the Blues.
While Italy great Totti expected Lukaku to move elsewhere, he says the potential return of a man who scored 30 goals in his final season with Inter would be a huge boost for the Nerazzurri.
"I wouldn't have expected it," Totti said. "I thought he was going to another club, but he wanted to go back to where he was good, he won [Serie A] and he wants to keep winning.
"In Italy he moves a lot, on a physical level it's embarrassing."
With Inter also reportedly targeting former Juventus man Paulo Dybala and hoping to keep hold of Lautaro Martinez, Totti said that such a level of depth would strike fear into opponents.
"No one knows with which tandem they will play, Simone Inzaghi will be happy." the Roma legend said.
Totti welcomed the arrival of Nemanja Matic at Roma as Jose Mourinho strives to build on its UEFA Europa Conference League triumph.
"If Mourinho made this choice it means that he is flexible for the team. We are talking about a great player who has shown his worth in Europe," he said.
"To come to Rome you need the right mentality and he has always shown that he has it."
Lille's Zeki Celik and Sassuolo's Davide Frattesi i have also been linked with the Eternal City giants and Totti says the Giallorossi need more strength in depth in order to push for a UEFA Champions League spot.
"To obtain results you always need great players. If these names are available to Mourinho, it will be a more competitive Roma, who wants to aim above all for a place in the Champions League," he added.
"Then he will have to buy other players to get what we have won in the past. As I've always said, you need champions to win."