During what the New York Times described as a wide-ranging, two-hour interview, the paper said Trump also appeared to lift a threat to take military action against Venezuela's neighbour Colombia.
Trump invited Colombia's leftist leader, whom he had previously called a "sick man", to visit Washington.
"Only time will tell" how long the United States would oversee Venezuela, Trump said.
When asked by the newspaper if it would be three months, six months, a year or longer, Trump said: "I would say much longer."
"We will rebuild it in a very profitable way," Trump said of Venezuela, where he sent troops to seize President Nicolas Maduro in a night raid on January 3.
"We're going to be using oil, and we're going to be taking oil. We're getting oil prices down, and we're going to be giving money to Venezuela, which they desperately need."
Trump said the US was "getting along very well" with the government of the interim president, Delcy Rodriguez, a longstanding Maduro loyalist who had served as the ousted leader's vice-president.
The Times said Trump declined to answer questions about why he had decided not to give power in Venezuela instead to the opposition, which Washington had previously considered the legitimate winner of an election in 2024.
Trump on Tuesday unveiled a plan to refine and sell up to 50 million barrels of Venezuelan oil that had been stuck in Venezuela under US blockade.
He declined to comment when asked if he had personally spoken to Rodriguez.
"But Marco speaks to her all the time," he said, referring to Secretary of State Marco Rubio.
"I will tell you that we are in constant communication with her and the administration."
The Times said its reporters were permitted to sit in during a phone call between Trump and Colombia's President Gustavo Petro, provided the contents of the call were off the record.
In a post on social media, Trump said: "It was a great honor to speak with the president of Colombia, Gustavo Petro, who called to explain the situation of drugs and other disagreements that we have had. I appreciated his call and tone, and look forward to meeting him in the near future."
Petro described the call, his first with Trump, as cordial.
On Sunday Trump had threatened to carry out military action against Colombia, calling Petro "a sick man who likes making cocaine and selling it to the United States, and he's not going to be doing it very long".
The Times said Trump's phone call with Petro lasted about an hour and "appeared to dissipate any immediate threat of US military action".
Trump has said the United States intends to "run" Venezuela.
US officials have indicated their plan for now is to exert influence without a military occupation.
Venezuela, with the world's biggest proven oil reserves, has become impoverished in recent decades, with eight million people fleeing abroad in one of the world's biggest migration crises.
Washington and the Venezuelan opposition have long blamed corruption, mismanagement and brutality by the ruling Socialist Party.
Maduro blamed the economic damage on US sanctions.
Several senior US officials said on Wednesday that the United States needed to control Venezuela's oil sales and revenues indefinitely in order to restore the country's oil industry and rebuild its economy.
Trump is scheduled to meet with the heads of major oil companies at the White House on Friday to discuss ways of raising Venezuela's oil production.
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