The Australian Taxation Office is chasing unpaid taxes of approximately £1.76million from Nathan Tinkler's Hunter Sports Group, which owns the Jets and NRL club the Newcastle Knights.
Federal Court documents filed in Sydney on Wednesday revealed Australia's Deputy Commissioner of Taxation had applied for the winding-up order with a hearing date reportedly set for February 20.
In a statement on the Jets website they claimed the ATO would be paid in full before that date and that it remained "business as usual".
Despite that Football Federation Australia chief executive David Gallop has met with senior officials for Tinkler, a Singapore-based mining magnate, over the past two days to ensure the club's viability.
The Jets' tax bill is reportedly less than half of the total amount owing with Gallop hopeful a repayment schedule can be agreed.
"The FFA has been given assurances by Hunter Sports Group, owner and operator of the Newcastle Jets, that the club's operations will not be affected," Gallop told The Australian.
It had been alleged some payment to the Knights players had been missed but members from the Jets, who suffered a fourth defeat in five games 3-0 at Perth Glory on Friday, confirmed they have so far been paid in full.
"We've just got to go out there and do our best, and things will either work out or won't," stand-in captain Ruben Zadkovich said.
"I don't think the Newcastle Jets are in any danger at the moment."
Former England international Heskey, 34, signed a one-year deal with the A-League club in the summer and has scored five goals in 11 appearances.