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In the days after Donald J. Trump was re-elected president, one of his most high-profile stops was at an Ultimate Fighting Championship event at Madison Square Garden.

Mr. Trump’s appearance in the front row was notable, as was the presence of some of his closest confidants, like Elon Musk, who sat alongside him. But few in attendance for the fights would have recognized the other man sitting beside the president-elect.

Yasir al-Rumayyan, the governor of Saudi Arabia’s vast sovereign wealth vehicle, the Public Investment Fund, watched the action from ringside, and is getting even closer to being part of the action. A company owned by the fund is close to creating a boxing league with TKO, the owner of Ultimate Fighting Championship. A deal for what would be a new competition, featuring up-and-coming boxers tied exclusively to the league, could be announced within weeks, according to three people familiar with the matter.

TKO said in a statement on Wednesday that it had “nothing to announce,” but that it “would evaluate any unique and compelling opportunity that could fit well in our portfolio of businesses and create incremental value for our shareholders.”

The wealth fund did not comment.

The potential investment in TKOfollows a Saudi Arabian effort in June to create a multibillion-dollar boxing league that would aim to unite the world’s best boxers, who for decades have been divided by rival promoters and fighting for titles controlled by an alphabet soup of sanctioning bodies. That effort, while not completely abandoned, had proved complicated and expensive, even for a country like Saudi Arabia, which for the past half decade has disbursed billions to become a player across some of the world’s biggest sports.

The investment in the new league will be made by Sela, a subsidiary of the Public Investment Fund. TKO — which is majority controlled by the entertainment and sports conglomerate Endeavor and embodied by Dana White, the U.F.C. empresario, a longtime friend of Mr. Trump’s — would be a managing partner. In return, TKO has been offered an equity stake and a share of the revenue, according to the people familiar with the matter, who spoke on the condition of anonymity ahead of the official announcement.