Trump has called for "extreme vetting" of refugees entering the United States along with a ban against people from "terrorist nations."
Trump's meeting with Sisi will take place at the end of the day, according to a campaign official.
He was supposed to travel first to Fort Myers, Florida for a rally.
He had alluded to meetings with foreign leaders in an interview with Fox television earlier in the day.
"I don't want to comment specifically on who but a couple of people are coming over. I've already met with a couple," he said.
But the meeting with Sisi appeared to be a response to Clinton, a former secretary of state who announced last week she would be meeting with the Egyptian leader as well as Ukraine's President Petro Porochenko.
Clinton has said she would discuss "the threat from terrorism" during her meeting with Sisi, who came to power after a bloody crackdown on political Islamists and has often warned that religious extremism presents a vital threat to the Muslim world.