Fred of Man Utd battles with Kevin de Bruyne of Man City during the Carabao Cup Semi Final match between Manchester City and Manchester United at the Etihad Stadium on January 29, 2020 in Manchester, England
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.
Reporting from Reuters
Liverpool v Everton? Manchester derby? Leicester v Aston Villa?
The rule stipulating players must be within 90 minutes driving distance from the venue of choice throws open the potential for a number of 'friendly' derbies.
It feasibly allows for any combination of teams from the north west - Liverpool, Everton, Manchester City, Manchester United and Burnley - to meet, while in the Midlands Leicester City may fancy a friendly against Wolves or Aston Villa.
There are then five London clubs, plus Watford, in the south east, while Brighton and Bournemouth could meet somewhere in the middle. Even a Sheffield United v Newcastle United friendly could take place, on a pitch (or in a field) just off the A1.
It's time to get the compasses out...
It may be difficult for Newcastle to arrange a friendly with another Premier League side
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Opinion: Why Tottenham could be the big winners from lockdown
A year after Tottenham's limp defeat in the Champions League final, there are still signs they could prosper in the new football climate...
Twelve months have passed since Moussa Sissoko's arm sparked a domino effect that ended with a Jordan Henderson jig and a red-ribboned trophy.
But as Liverpool prepare to take another triumphant step, this time in the Premier League, Tottenham are still tripping over their feet as the spectre of mediocrity looms large once more.
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Gone is Mauricio Pochettino, the architect of their latest revival. In is Jose Mourinho, a man haunted by his two most recent spells in England and who, before lockdown hit, was staring at a dour third. There is a plush stadium but no signs of a fortress. Big money signings but little end product. Out of all competitions. A place in the top four a distant dream.
But distant dreams may be enough. Tottenham, even for their lengthy rap sheet, are still in an enviable position. Their refusal to diverge from a strict wage structure looks smarter by each passing month, even if they feigned financial vulnerability by fleetingly pressing the furlough button. They are not sandbagged by players on £300,000 a week, nor are they chasing replacements as the squad that stunned Borussia Dortmund, Ajax and Manchester City in 2019 remains largely intact.