The cheerful tones come after the two leaders spoke on the phone on Monday.
Trump describes the conversation in a post on Truth Social as "very good" and continues:
"We will have continued discussions and we will meet in the near future, both in Brazil and the USA", the post says.
The American president has introduced tariffs of 50 percent on Brazilian products and issued sanctions against several tops, including a judge in the Supreme Court, in order to punish what Trump calls a "witch hunt" against the country's former leader Jair Bolsonaro.
"We are very optimistic about moving towards a situation that benefits both parties", says Brazil's Vice President Geraldo Alckmin, who has been tasked with continuing the negotiations with the US Secretary of State Marco Rubio.
The relationship between the countries became strained when Trump in August made good on his tariff threat, but improved again when Trump and Lula ran into each other at the UN General Assembly in New York last week.
