The campaign was suspended indefinitely after the country was blocked in the midst of the coronavirus crisis.
On Friday, the 20 Premier League clubs held a video conference to try to find a way to end the current season.
Some clubs still have 10 league games to play, while there are also national and European cup competitions to be completed.
The return to full training is not yet complete, as players perform personal routines instead.
FIFA have reportedly extended the season indefinitely, which would complete the Premier League this summer.
However, the new campaign is expected to start on August 8, although this date may be extended.
Daily Mail staff say Premier League clubs have been warned that there could be as little as a two-week break between seasons as they seek to get the soccer calendar back on track.
It is believed that players would not need a full pre-season as they would already be in shape by the end of this campaign.
However, experts have warned players to increase the risk of injury if games are crammed to end the season, and the move may heighten concerns for their well-being.
Meanwhile, the Premier League has reiterated its intention to end the season.
A statement said, “It has been recognized that the Premier League will not resume in early May – and that the 2019/20 season will not return until it is safe and appropriate.
“The restart date is constantly being reviewed with all stakeholders as the impact of the COVID-19 pandemic grows and we work together during this very difficult time.
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“The Premier League works closely with all professional football in this country, as well as with government, public agencies and other relevant stakeholders to ensure the game results in a collaborative solution.
“With that, there is a combined target for all national league and cup games to play, allowing us to maintain the integrity of each competition.
“However, any return to play will only be with the full support of the government and when medical advice allows. “