Under the current system, someone who is denied a taxi licence by a local authority in England and Wales can travel to another area where the licensing authority may be more lenient.
Other proposed safety measures include a recommendation that councils ensure every driver undergoes background checks and enhanced criminal record checks.
The consultation will run until 22 April.
Taxis minister Nusrat Ghani said: “While the vast majority of drivers are safe and act responsibly, we have seen too many cases where taxi and minicab drivers have used their job to prey on vulnerable people, women and children.
“These rules would make sure that drivers are fit to carry passengers, keeping people safe while stopping those with bad intentions from getting behind the wheel of a taxi or minicab.”