The Welsh club ower £2.1million, of which £1m is to the inland Revenue.
They will receive a jackpot of £75,000 as a result of tonight's Cup clash being televised.
Former Wales manager Mark Hughes, who is from Wrexham, has offered his support to the club.
Hughes, now Blackburn manager, said: "Everyone in football has been really disappointed with the situation that has developed, and having come from there I probably know as much as anyone how much it means.
"I was born just down the hill from the football club and my children were too. The Racecourse Ground is a fantastic facility and for that to be taken away from the community would be a crying shame.
"Hopefully going into administration will give them the breathing space they need - it is probably the only way they can survive.
"Wrexham is a great football club and the facilities they have are outstanding for the level they play at.
"At least they do have the benefit of a very good manager in Denis Smith and although it will be very difficult for them to stay up after the 10-point deduction it should be possible with the players and management team they still have."
Controvesial club owner Alex Hamilton has refused to accept a takeover bid fronted by former chairman Mark Guterman. He turned down the latest takeover offer from Guterman and his consortium on Tuesday, with suggestions that the current owner is keen to put the club into liquidation and redevelop The Racecourse Ground into commercial property.
By petitioning to go into administration, the club avoided the deadline of an Inland Revenue winding-up order, which had been set for Wednesday and could have sent them out of business.