Aides to the former New York City mayor reached out to discuss ways the two entrepreneurs-turned-politicians could work together as Mr. Bloomberg seeks the Democratic nomination, these people said.

Mr. Yang, who dropped out of the race earlier this month, didn’t commit to join forces, as he considers his own political future, a third person familiar with the discussions said.

Mr. Yang didn’t immediately respond to a request for comment. A senior Bloomberg aide said Mr. Yang wasn’t being seriously considered to be the former mayor’s running mate if he secured the nomination.