Mr Bashir will travel to Saudi Arabia on Friday, Sudan's Foreign Minister Ibrahim Ghandour said.
The minister added that he hopes US sanctions against Sudan will be lifted in July, and said he believes the US wants to normalise relations.
The US has not confirmed the claim.
Economic sanctions were imposed against Sudan in 1997 after the state was labelled a "sponsor of terrorism".
President Barack Obama signed an executive order easing some of the curbs in January, shortly before leaving office.
The White House said the move was intended to acknowledge Sudan's efforts to reduce internal conflict, improve humanitarian access to people requiring aid, and curtail "terrorism".
Mr Obama had delayed the reduction in sanctions by 25 weeks, to give the Sudanese government an incentive to continue its reforms.
Relations between the US and Sudan have not been tension-free of late, however.
The country was one of seven included in Mr Trump's proposed travel ban, along with Iran, Iraq, Libya, Somalia, Syria and Yemen.
It is not known whether Presidents Bashir and Trump will meet when the US leader arrives in Saudi Arabia on Saturday.
The visit is Mr Trump's first overseas trip since taking office, and he is scheduled to address the summit on his "hopes for a peaceful vision of Islam".
In 2009 and 2010, the International Criminal Court issued arrest warrants against Mr Bashir for genocide, war crimes, and crimes against humanity related to the conflict in Darfur, which has claimed at least 300,000 lives.
He denies the charges, and has successfully evaded arrest for several years.
The ICC is based in The Hague, and was established in 2002 to try the world's most grievous crimes, when national courts are unable or unwilling to act.
A US official told NBC News that the Trump administration opposes invitations or travel by individuals facing ICC indictments.
"The United States has made its position with respect to Sudanese President Omar al-Bashir's travel clear," the official said.
"While the United States is not a party to the Rome Statute, which is the treaty that established the International Criminal Court, we nevertheless strongly support efforts to hold accountable those responsible for genocide, crimes against humanity, and war crimes, including such acts in Darfur," the official added.

The force confirmed it was examining a number of buildings used for firearms training between 1980 and 2007.
It also said it was in the process of contacting "a large number of officers" who might have been affected.
At one time asbestos was frequently used as a building material.
Exposure to asbestos can cause serious and potentially-fatal diseases including mesothelioma, lung cancer and asbestosis.
It is thought it is generally only people who regularly work directly with materials containing asbestos who are at any serious health risk but Health and Safety Executive figures estimate there are 5,000 deaths a year caused by exposure to the substance.
Short-term exposure is not considered to pose a danger.
The HSE says asbestos can be present in any building built or refurbished before 2000.
The Met said it would undertake rigorous examinations at all buildings where firearms training took place to establish whether asbestos was present.
Ch Supt Mike Gallagher said officers still working for the force had been contacted.
He said inquiries had identified a possible issue at some buildings used historically and detailed investigations had been carried out to identify all those individuals potentially affected.
"Due to the time period in question and number of possible sites, we need to make contact with a large number of officers," he added.
"This will include those who have left, retired, or transferred, so clearly this is a process which will take some time."
Professor John Cherrie, of Heriot-Watt University in Edinburgh, who has worked on several asbestos research projects, said most people were exposed to low levels of asbestos at some time during their life.
"However, people who become ill from asbestos are usually those who were exposed to it on a regular basis, most often in a job where they worked directly with asbestos-containing materials."
Saudi Arabia has invited Sudanese President Omar al-Bashir, who is wanted for alleged war crimes, to a summit with US President Donald Trump and Arab and Muslim leaders.
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Up to 30,000 police officers might have come into contact with asbestos at training facilities, the Metropolitan Police have said.