Relations between the two countries soured following the overthrow of former Egyptian President Mohammed Morsi, a close ally to the Turkish government, in 2013, leading to President Abdel Fattah al-Sisi to take over as leader.
President Recep Tayyip Erdogan repeatedly condemned the ouster as a "coup d'etat" against Morsi.
He has also shown solidarity at rallies by flashing the four-finger "Rabaa" hand salute, seen as a symbol of the Muslim Brotherhood.
"We think we need to develop economic and cultural ties with Egypt as countries that use the two sides of the Mediterranean," Yildirim told reporters at a briefing in Istanbul.
However, he sounded a note of caution that high-level relations would not be repaired overnight.
"We think we need to start from somewhere," he said.
It is not the first time Yildirim has expressed hope for improved relations with Egypt.
In June, he said he did not want to see "permanent enmity" with countries such as Egypt and Syria.
Saudi Arabia, one of the main backers of Egyptian President Abdel Fattah al-Sisi, is keen to see the two countries reconcile as it grows increasingly close to Turkey.
After the 15 July failed putsch in Turkey by a rogue military faction aiming to oust Erdogan from power, Egypt's presidency remained mute.
However, the foreign ministry released a statement on consular efforts to help Egyptians in Turkey.
Turkey appears to be taking steps to return to its former "zero problems with neighbors" foreign policy after rapprochements with Russia and Israel in June this year.
Comment: Yildirim sure has been busy patching up old ties in the Middle East: