City had been due to face a winding-up petition on Monday, but Cox told BBC Radio Oxford it will not now be heard.
A judge could have passed a winding-up order that would have liquidated the 134-year-old club.
Oxford are next to bottom in National League South, having won only one of their eight games so far this season.
It has been a turbulent few months for the club, with former club president Thomas Guerriero jailed for fraud in May and managing director Colin Taylor found dead at the club's stadium in July.
Oxford City chairman Brian Cox has confirmed that a pending High Court hearing has been called off after the club paid an outstanding tax bill.