Guterres, who met with Russian President Vladimir Putin at the end of last month, said he hoped for a similar outcome with the American President-elect.
The former Portuguese prime minister takes over from Ban Ki-moon on January 1 amid ongoing bloodshed in Syria and questions over the US role in the world under a Trump presidency.
"I had an excellent working meeting with President Putin and I hope this will also be the case with Donald Trump," he told Portuguese television channel SIC in an interview Wednesday.
"It is certainly in my interest to visit him as soon as possible," he said. "The United States is not only the main donor of the United Nations but a fundamental element in its actions."
Trump on Friday said Washington's policies at the UN will be different after he takes office.
"As to the UN, things will be different after Jan 20th," he said on Twitter, referring to the date of his inauguration.
The tweet came after the United States refrained from vetoing the adoption of a Security Council measure calling on Israel -- its closest Middle East ally -- to halt settlement activities in Palestinian territory.
Guterres said he was "determined to establish a constructive dialogue with the future American administration".
Trump has not hidden his scepticism about the fight against global warming but has modified that position since his November 8 election win saying he may support global accords on climate change, and that he had "an open mind".
Asked about this, Guterres said the "new (US) government will certainly adopt a different position" than that of Barack Obama's administration.