A document posted online by WikiLeaks appeared to show a March email in which campaign chairman John Podesta offered a wide list of potential vice presidential picks, also including a retired Navy admiral and Sen. Bernie Sanders.
Podesta, noting that he and a small group had done a "first cut of people," offered the list organized "in rough food groups."
Bloomberg, who founded Bloomberg LP and is a former New York City mayor, spoke at the Democratic National Convention in July in support of Clinton.
The groups apparently organized by Podesta included Hispanic male officials, female officials, white male officials, black male officials, retired military officials, private sector leaders — and Sanders.
Although many of the political names on the list were unsurprising, the private sector options may offer some insight into the campaign. In addition to Bloomberg, Cook, Schultz and the Gateses, those names were:
Disclosure: Judith Rodin serves on the board of directors of Comcast, parent company of CNBC.