The England & Wales Cricket Board is set to launch a tender for domestic rights this autumn, according to the Daily Telegraph newspaper.
According to the report, the national body has told interested parties that the tender process will take place earlier than originally planned.
The rights will be available from 2020.
In 2012, pay-television broadcaster Sky agreed to pay between £60m (€78m/$91m) and £65m per year for ECB rights over four years, from 2014 to 2017. That deal included an option for Sky to renew at about £75m per season for 2018 and 2019.
The newspaper added that pay-television broadcaster BT Sport is likely to challenge Sky for the rights.