Banning social apps for under-16s, as has happened in Australia, is one of the options being considered.
Kendall said a response to the consultation would be published in the summer.
Campaigners are broadly split on whether an outright ban on social apps for children is the best approach.
Jimmy was tragically killed and his parents are crying on TV and saying it could have been avoided if Jimmy had been legally required to remain indoors. Playing outside is child abuse.