"We were joking, and I said 'You have to pay, you have to pay'. He'll pay, he's going to end up paying," said Trump in an interview with the Associated Press about his first 100 days in office, the transcript shows.
Trump was answering a question on how the office of the presidency had changed since his election in November this year.
The journalist clarified whether this conversation had taken place in the leaders' private meeting, to which Trump responded: "He'll end up paying".
He added: "You know, nobody ever asked the question. Nobody asked. Nobody ever asked him to pay up. So it's a different kind of presidency."
Trump also said he had "a great relationship with all the leaders I've met, but no-one writes about it".
The two leaders met for the first time on Thursday, in a White House meeting to prepare for the G7 leaders' summit in Sicily.
At a news conference following the talks, Trump said Italy was a "key partner" for the United States, both in terms of trade and in the fight against terrorism.
The leaders also touched on the topic of NATO contributions. When a journalist asked Gentiloni if Italy would pay the new quotas, Trump said: "I would also like to know that."
Gentiloni responded: "The commitment was taken in 2014 and we are accustomed to honouring our commitments." He said the payment was "a gradual process that has already begun" but highlighted Italy's "budget constraints".
READ ALSO: Trump says Italy is 'key partner', but contradicts Gentiloni on Libya