The two midweek games would take every team up to 29 matches, with the weekend of June 20-21 then set to hold the first full round of fixtures, the Telegraph reports.
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After contact training was given the green light earlier this week, clubs discussed on Thursday how the league can restart following its suspension in March due to coronavirus.
The latest meeting covered a range of subjects, including the fixture list and match venues, with a debate about playing games at neutral grounds yet to be resolved.
The report means Premier League managers have three weeks to prepare their squads for a return to action.
Sterling: Weeks of training needed before restart
Early August finish for Premier Leauge?
The proposal would also see the league finish on the weekend of August 1-2, allowing for the FA Cup final to take place the following weekend.
That would allow time for UEFA’s competitions to conclude, with the governing body having previously stated their desire to finish the Champions League and Europa League by the end of August.
Phase Two gets the green light
On Wednesday, Premier League clubs voted unanimously to return to contact training, including tackling.
A statement, following a meeting of all 20 clubs, said: "Squads are now able to train as a group and engage in tackling while minimising any unnecessary close contact.
Clubs last week returned to training in small groups without contact and under strict health protocols.
Phase Two allows up to 10 players to work together and would ease the time restrictions on training sessions and allow players to be closer.
The third phase would be a move to a more typical form of training in the build-up to actual games.