Amazon.com Inc. is considering whether to use its Alexa virtual assistant to start a person-to-person payments feature, a move that would push the retailing giant into new competition with PayPal Holdings Inc.’s Venmo and big banks’ payments efforts, according to people familiar with its strategy.

The Seattle company, which has expanded from online commerce to cloud computing and entertainment, is exploring new ventures and capabilities that could give it more power in a payments industry currently dominated by banks and card...