Clubs across steps 3-6 of the non-league pyramid have been canvassed as to whether they want to use the competition to return to match action once outdoor team sport can resume on March 29.
So far, Baffins Milton Rovers and Horndean have said they definitely won’t be entering.
And Moneyfields could be another absentee as they still haven’t appointed a new manager yet.
The five names on the club’s shortlist to replace Dave Carter - who quit to join AFC Portchester last month - have all been interviewed.
Chairman Pete Seiden said today that the club’s nine-man board will be convening on Thursday with a view to picking what will be only Moneyfields’ third manager since 2003.
He added: ‘We’re considering whether to take part in the Invitational Cup.
‘It could be that if we do enter we’d look to play a mixture of the first team and reserves.
‘We’re still waiting to see whether the reserves will be restarting (their Hampshire Premier League) season.’
Portland United are another Wessex Premier club who have said they won’t be taking part in any Invitational Cup.
Wessex League secretary Greg Dickson holds a similar position with Moneyfields’ Southern League Division 1 South rivals Sholing.
Dickson said: ‘We’re going to have a meeting about whether to enter the cup tonight.
‘The problems we have go across the board - we don’t yet know whether fans will be allowed in, and clubs need that income.’
At present, fans aren’t allowed inside sports grounds under the Government’s roadmap out of lockdown until May 17.
The FA, though, are in talks to see if an exception can be made for grassroots football matches prior to that date.
‘We’ve also got to give up our pitch on May 1 due to cricket,’ Dickson added.
The Invitational Cup is scheduled to start on the first weekend after Easter, on Saturday April 10, comprising comprise geographically based groups followed by a knockout stage.
A maximum of 47 clubs could have entered – the 39 Wessex League clubs plus Southern League outfits Gosport, Moneyfields, Farnborough, AFC Totton, Sholing, Winchester, Basingstoke and Hartley Wintney.
Gosport, Portchester, Fareham and US Portsmouth have all said they are happy to take part - though the latter two said fixtures must be worked around their FA Vase commitments.