Venues must not be more than 90 minutes away and players will need to travel in their own cars and arrive in full kit, according to Sky Sports.
Matches will be refereed by members of the clubs’ coaching staff and players involved need to have returned a negative test for Covid-19, the reports said.
The Premier League, which has nine rounds remaining, has been suspended since mid-March but clubs have since returned to group training, with the government giving elite sport permission to return from June 1.
No Premier League matches have been held since March 9, since third-placed Leicester City’s 4-0 thrashing of relegation-threatened Aston Villa at the King Power Stadium.
Yet while players have kept fit at home and have now been back in training since May 19, they are still searching to rediscover their match fitness.
Leicester City manager Brendan Rodgers said the Midlands club will stage practice games at the King Power Stadium to help their players get up to speed.
“We’ll look at trying to prepare as best we can for that. We’ll have some practice games in our own stadium before we play, so they’ll feel and get a sense of that,” Rodgers told British media.
It is thought that several Championship teams have had requests from Premier League clubs to play friendly matches already.
Liverpool and West Ham have already held squad friendlies at their own stadiums in recent days.