The Securities and Exchange Commission (SEC) is seeking to find out whether Arora had conflicts of interest or engaged in questionable behaviour, Bloomberg News reported, citing unnamed people familiar with the matter.
The watchdog was also eyeing SoftBank's disclosures to investors, it said, adding that the inquiry was a preliminary step and does not guarantee further action against the company or its former executive.
"SoftBank Group does not comment on press reports of (US) regulatory inquiries," the company said in a statement on Thursday in response to the report. India-born Arora, once seen as SoftBank boss Masayoshi Son's heir apparent, stepped down last week just two years after being plucked from a high-profile job at Google.
Son told an annual shareholders meeting he had changed his mind about the timeline for stepping down to make way for right-hand man Arora. Both men said it was an amicable split, and Arora would stay on as SoftBank advisor.