The former Egyptian army chief had strained relations with outgoing President Barack Obama's administration, which had temporarily suspended military aid after Sisi toppled his elected predecessor in 2013.
"Personally I respect and appreciate" Trump, Sisi said according to an English translation of his remarks to Portuguese news agency LUSA published on Saturday.
"I believe that President-elect Trump will be more rigorously engaged with the issues of the region," he said.
"As a matter of fact President-elect Trump has shown deep and great understanding of what is taking place in the region as a whole and what is taking place in Egypt," he added.
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"That is why I am looking forward, and I am expecting more support and more reinforcement of our bilateral relations".
Trump's tough-on-terrorism rhetoric has appeal among Egyptian officials, as the country faces a jihadist insurgency that has killed hundreds of policemen and soldiers.
The insurgency took off after the military overthrew Islamist president Mohamed Morsi in 2013, unleashing a deadly crackdown on supporters.
Sisi, who had met Trump in September in New York, downplayed Trump's calls to ban or extremely vet Muslims entering the United States.
"We have got to draw a distinction between the rhetoric that takes place within presidential campaigns and the real and actual administration of a country after the inauguration of a president," he said.