It has been given to the Ambassador Alice Wells on Tuesday. It is unclear.
Afghan officials have been discussing how to handle a possible US withdrawal and would that be aware that cost-saving would be attractive to Trump.
However, the letter did not suggest a specific time for the CNN.
The letter did not suggest a specific time for the meetings in the near future, "the sources added.
Ghani invited Trump to come to Kabul at the "near future" for discussions.
At the time, the State Department officials said that it was in the works at the time of last year's UN General Assembly the timing had not been worked out for the upcoming elections, implying that both sides wanted to delay.
Earlier this week, the US Special Representative for Afghanistan said that it had agreed in principle for a framework to talks that could end up being nearly 20-year.
Zalmay Khalilzad said the framework for peace would be the cause for peace in Kabul, Zalmay Khalilzad a US military withdrawal.
"We have a draft of the framework that has fled before it becomes an agreement," Khalilzad told the Times on Monday.
The Pentagon is currently discussing a withdrawal from these lines, but the plan hinges on talks between the United States Afghan President and the Taliban, according to Trump administration officials.
The US has about 14,000 troops in the country, most of which are present as part of a larger NATO-led mission to train, advise and assist Afghan forces.
CNN's Jennifer Hansler and Eli Watkins contributed to this report.