The fund was set up in 2017 and has become one of the primary funding vehicles for technology companies around the world.
SoftBank is also in talks with Oman for an investment in the fund, which has raised nearly all of its funding so far from Saudi Arabia and Abu Dhabi, according to the report.
Oman was not immediately available for a comment requested by Reuters, nor was there an immediate response from the Japanese conglomerate.
SoftBank is seeking to raise new funds for "informal deals" chief executive officer Masayoshi Son negotiated in China for Vision Fund, one of the people told WSJ.
The fund is also planning to double its staff over the next 18 months to keep up with the pace of deal making by SoftBank, the company's top deputies reportedly said at a conference in Los Angeles this week.
The company has publicly stated it plans to set up a second investment fund, and according to the WSJ story, is talking to banks about helping it raise some money.