The fresh investment would form part of a funding round that could raise up to $100 billion for OpenAI, valuing it at about $830 billion, the person said.
The source declined to be identified, as the information had not been publicly disclosed.
Seeking to improve SoftBank's position in the artificial intelligence race, Chief Executive Masayoshi Son has made an "all-in" bet on OpenAI. In December, SoftBank said it had completed a $41 billion investment in OpenAI, giving it an 11% stake.
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OpenAI is grappling with rising costs to train and run its AI models as competition from Alphabet's Google ratchets up.
The news was first reported by the Wall Street Journal.
SoftBank, whose shares were up 3.5% in Tokyo morning trade, declined to comment.
Reuters reported last month that Son had scrambled to marshal the funds for the previous investment, slowing most other dealmaking at SoftBank's Vision Fund to a crawl.
Both OpenAI and SoftBank are also investors in Stargate, a $500 billion initiative to build AI data centres for training and inference that executives say is crucial to the US government's ambitions to keep ahead of China in AI.
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