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Welling joint-owner Barrie Hobbins is hopeful of resolving the club's future before they are due to appear in the High Court next week.
The Wings revealed last Thursday that they have been served with a winding-up petition by HMRC, who they owe nearly £90,000.
But Mr Hobbins (pictured) is hoping that a repayment plan can be put in place later this week, with the club having already paid more than a third of the money due.
"I've spoken to a specialist who deals with this, based in Leicestershire, that we've been put in touch with through a season-ticket holder," said Mr Hobbins.
"They've asked me to provide a realistic payment plan to put forward to HMRC.
"We're expecting to have a further £15,000 (for HMRC) this week, on top of the £30,000 already paid, and then have a plan in place for the remainder.
"This company will go back to HMRC and negotiate, hopefully, a sensible deal.
"Hopefully that would be resolved before this weekend. I can't say I expect it to happen as it does depend on someone else saying yes or no."
Mr Hobbins has been heartened by the response of the club's fans, with more than 100 attending an open meeting at Park View Road on Saturday where more than £4,000 was raised in donations.
The Wings have also been approached by as many as six potential new investors, although talks are still believed to be at an informal stage.
Mr Hobbins added: "I've never assumed it was all doom and gloom. There's the possibility that we can reach agreement, and that's quite common.
"There's no point closing down a business if you can get your money back.
"I've sent 18 pages of cashflow and projections through and we're hoping to have the petition dismissed or adjourned."