Masayoshi Son made the comments to the media as the Japanese technology giant reported a 50% rise in quarterly operating profit.
It is the first time the group has said it is interested in Uber.
Softbank has already invested in Asian ride-sharing firms Grab and Didi Chuxing.
Mr Son, who founded the company in 1981, described the US as "the most important market".
"We are interested in discussing with Uber. We are also interested in discussing with Lyft," he said, but added that he hadn't decided "which way" to go.
"Whether we decide to partner and invest into Uber or Lyft, I don't know what would be the end result," he said.
"We are definitely very much interested in the US market."
Softbank has already shown an appetite for ride-sharing and backs China's Didi Chuxing.
Last month, the company joined with Didi Chuxing to pour $2bn (Â£1.5bn) into Grab, South East Asia's most popular ride-hailing firm.
As an early investor in Alibaba, Mr Son has a reputation for spotting potentially transformative industries and trends.
In 2016, Softbank partnered with Saudi Arabia's sovereign wealth fund to launch a technology fund worth as much as $100bn.
The company also has stakes in a number of British technology firms including virtual reality firm Improbable.
Softbank's chief executive has said he is considering investing in Uber or Lyft, as the company eyes a move into the US ride-sharing market.