Saints could be back in action in July
Any resumption is subject to government approval, with the next review of lockdown measures set to be announced to the public on May 7.
The Gallagher Premiership was initially suspended for five weeks on March 16 because of the Covid-19 pandemic that has swept the globe.
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Hide AdThe suspension was extended indefinitely on April 8 and Premiership Rugby is now said to be drawing up plans to play games behind closed doors in bio-secure environments.
According to Sky Sports, it could mean all games being played at one or two venues, with on-site coronavirus testing required and with midweek matches essential to complete a fixture list on which all 12 Premiership clubs have nine matches outstanding.
Players are expected to require four weeks of training before returning to action, which would mean a return to the club in June.
This best-case scenario would result in the Premiership final being played in mid-August.
Saints are currently fourth in the Premiership, having won seven of their 13 league matches so far.