Speaking on a visit to Japan on Sunday Trump said he "just spoke to the king a while ago and they will consider it". It comes a day after he tweeted that he would "very much appreciate" it happening, adding that it was "Important to the United States".
The listing of part of the state oil company will likely be the biggest IPO in the world. It's scheduled to take place int 2018.
Trump expanded upon his tweet on Sunday, telling journalists that “It’s very important. We want to have all the big listings”.
He said he wanted Saudi Arabia to "strongly consider the New York Stock Exchange or Nasdaq or frankly anywhere else located in this country” and that it had not been considering it because of "litigation, risk and other risk”, AFP reports.
Just a small fraction of the company is expected to go public, potential as a dual listing on the Tadawul, the Saudi stock exchange and another international exchange.
London is one of several cities vying for the business.
The boss of the UK's Financial Conduct Authority Andrew Bailey was this week forced to defend the regulator in front of MPs. He rejected claims that changes to listing rules for sovereign controlled companies were influenced by the government to attract the listing.