Trump's envoy to the Middle East, Jason Greenblatt, reportedly raised the initiative with Arab officials.
"One of the ideas that was raised in the Egyptian-American meetings in Washington is holding a peace summit hosted by the United States this summer," American sources told the London-based paper.
According to the report, the Trump administration expects Egypt, Jordan and the Gulf nations to play an active part in motivating the Palestinian side to return to the negotiating table.
During their White House meeting on Monday, al-Sisi presented to Trump the Arab nations' position on the conflict, which calls for a "just solution for the Palestinian issue based on the Arab peace initiative, and opposes moving the American embassy to Jerusalem."
Trump moved to reset US relations with al-Sisi after the prior Obama administration's strained ties, giving him firm backing and vowing to work together to fight Islamist militants.
"I just want to say to you, Mr President, that you have a great friend and ally in the United States, and in me," Trump said.
Sisi said he appreciated that Trump has been “standing very strong ... to counter this evil ideology.”
The American and Egyptian presidents discussed the renewal of annual joint training exercises between the two militaries, which have been put on halt following the ouster of former Egyptian Mohammed Morsi.
A joint statement said Trump and Sisi agreed that Islamist militants could not be defeated solely by military force. It said the leaders "agreed on the necessity of recognizing the peaceful nature of Islam and Muslims around the world."
While Trump noted the United States and Egypt "have a few things" they do not agree on, he made no public airing of US concerns about human rights in Egypt.
The trip was Sisi's first official US visit since being elected president in 2014. Trump's predecessor, Barack Obama, never extended an invitation.
Obama froze aid to Egypt for two years after Sisi, then a general, overthrew President Mohamed Morsi in mid-2013 after mass protests against Morsi's rule. Morsi, a Muslim Brotherhood member, had been elected the previous year.
The one-on-one meeting between Trump and Sisi, followed by a separate gathering with top aides, showed how intent the new US president is on rebooting the bilateral relationship and building on the strong connection the two presidents established when they first met in New York last September.
Reuters contributed to this report.