Rovers will host Everton U21 as part of the group stage of the EFL Trophy.
The young Toffees were drawn into Northern Group H which already contained Rovers, Burton Albion and Mansfield Town.
The first group game is set to take place on September 5 or 6. The others will follow on October 10 or 11 and November 14 or 15.
Rovers will host Everton U21 at the Eco-Power Stadium as well as one of Burton or Mansfield.
Full fixture details will follow in due course.