Erdogan on April 20 said in an interview with Turkish media that the meetings with Trump would be held May 16-17 after the Turkish leader travels to China on May 15.
'I will be travelling to China, and after China I will be traveling to the United States,' he said.
There was no immediate announcement from the White House on the visit.
Erdogan's visit will give him an opportunity to build on his relationship with Trump after a difficult period with the previous Obama administration.
Erdogan and President Barack Obama clashed over the U.S. administration's criticism of Erdogan's record on human rights, while Ankara was angered by U.S. support for Kurdish groups in Iraq and Syria.
Turkey has also been pressing Washington to extradite Fethullah Gulen, the U.S.-based Islamic cleric it accuses of being behind last year's failed coup.
Trump, on the other hand, was the only Western leader to phone Erdogan to congratulate him for winning a referendum that significantly strengthened Erdogan's ruling powers.
The referendum has been heavily criticized by Western countries, including the United States, for putting too much power into the president's hands and it has been challenged as flawed by the European Union and Turkish opposition figures.
'I hope and pray that this tete-a-tete meeting in the United States in May will lay the foundation for stronger cooperation,' Erdogan said in the interview.
He added it was "very early" to comment on his future relationship with Trump.
"When I met President Obama for first time I was very hopeful. Let's embark on this journey,' he said.
He added, though, that he had spoken with Trump three times by phone. 'Every time we spoke to one another I have become more hopeful,' he said.
On the demand that Washington extradite Gulen, Erdogan said, "I believe President Trump will do what President Obama failed to do.'
With reporting by AFP and Reuters