They have also suggested a Supplementary League Cup tournament, featuring all 31 clubs, which would start on April 10 and culminate with a final on May 29.
The cup would be on a Champions League style format with seven groups of four teams and one group of three teams playing each other home and away with the top two teams from each group progressing to the knockout stages.
Group games will be played between April 10 and May 1 - including two midweek rounds on April 14 and 21 - with the knockout stages starting on May 8. The quarter-finals (May 15), semi-finals (May 22) and final (May 29) follow on.
Group 1: Sway, Lyndhurst, Infinity, QK Southampton.
Group 2: Clarendon, Michelmersh, Netley, Broughton.
Group 3: Stockbridge, Andover New Street Swifts, Silchester, Overton.
Group 4: Kingsclere, South Wonston, Winchester Castle.
Group 5: Colden Common, Upham, Bush Hill, Chamberlayne.
Group 6: Locks Heath, Moneyfields Reserves, Fleetlands, Hayling United.
Group 7: Paulsgrove, Harvest, Clanfield, Denmead.
Group 8: Liss Athletic, AFC Petersfield, Liphook, Headley.
Clubs have until next Friday, March 21, to inform the league whether they want to curtail the season, and whether they want to compete in the cup competition.
Clubs have been told they cannot sign on any new players from higher division clubs - steps 3-6 of the pyramid having been curtailed last month by the FA.
The curtailment of the 2020/21 season means Infinity will have gone two campaigns without losing an HPL Senior Division match.
It also means clubs aiming to progress to the Wessex League will have to wait on any possible FA restructuring at the bottom of the non-league pyramid.
Infinity, Fleetlands, Bush Hill and Stockbridge have all applied for promotion, but that will depend on the FA promoting clubs from Division 1 of the Wessex.
There is one space available in Division 1, though, as Pewsey Vale - who withdrew in December 2019 - have yet to be replaced.