It is an ambitious project, designed on the back of falling global oil prices, that will see the country invest in businesses around the world while expanding non-oil businesses and small and medium enterprises at home.
The Nikkei business daily also reported that Toyota Motor is looking at building a auto assembly plant in the Middle East country.
The king's group is two to three times the size of the delegation led by his son, Deputy Crown Prince Mohammed bin Salman, that visited Japan in September past year.
Custodian of the Two Holy Mosques King Salman bin Abdulaziz Al Saud received at his residence in the Japanese capital Tokyo Governor of Tokyo Yuriko Koike.
Japan has offered to share its expertise in supply chain management, healthcare and renewable energy with Saudi Arabia, as the kingdom seeks to wean its economic dependency on crude oil.
"We would like to more aggressively develop relations with Saudi Arabia, the cornerstone of stability in the Middle East", Abe stressed during the meeting.
Saudi King Salman met with Japanese Prime Minister Shinzo Abe, the sides discussed ways to bolster Japanese investment and trade in the Saudi Arabia, possibly by setting up special economic zones there.
The IPO is the centerpiece of the Saudi government's ambitious plan, known as Vision 2030, to diversify the economy away from oil.
Also on Tuesday, around 20 Japanese companies, including Toyota, exchanged memoranda of understanding with Saudi Arabian companies and government to strengthen ties.
Abe made the request for support on the Aramco listing to the Saudi monarch, who responded by saying the kingdom would look into the request because he wants Japanese investors to buy Aramco shares, Japan's Deputy Chief Cabinet Secretary Kotaro Nogami told reporters.
In September past year, Emperor Akihito held talks with the king's son, Deputy Crown Prince Mohammed bin Salman, at the Imperial residence.
They had a meeting and lunch together at the Imperial Palace also in February 2014, when Salman was crown prince. King Salman will next visit China during his tour of Asia.