The 20-year-old spent part of last season on loan at Sunderland, but has been heavily linked with a move North of the border following the appointment of Steven Gerrard as 'Gers' boss.
Gerrard knows all about the midfielder from his time working in Liverpool's academy and he is thought to see the youngster as the ideal addition to his squad.
Ejaria has made eight appearances for the Liverpool first team and was part of the England squad that won the U20 World Cup in South Korea last year.
Should the deal be completed, Ejaria would become Rangers' fourth signing of the summer, following Allan McGregor, Jamie Murphy and Scott Arfield in making the move to Ibrox.