Parker said on Wednesday there is "no limit" to how Amazon is storing and listening to private conversations, adding that these recordings "could potentially be used against you in a court of law or for other purposes."

"If you're having a conversation in front of an Alexa-enabled device, Amazon is not guaranteeing you any privacy," Parker said in a discussion on stage with CNBC's Hadley Gamble at the Milken Institute MENA Summit.

Amazon came under fire last year when an Echo device reportedly secretly recorded a family's conversation and sent it to a random person. Amazon blamed the incident on Alexa misinterpreting a set of commands.

A spokesperson for Amazon told CNBC that customer trust is of the utmost importance, sit takes privacy seriously.