The Lilywhites were given a winding up order on Friday evening, with Shaw claiming the amount owed is just £400,000.
"At the moment we are having to bounce things off our financial advisors and listen to their advice. We're a bit limited about what we can say as we're a PLC and issues like this are share-sensitive," he told the Lancashire Evening Post.
"We were 20 days late with our payment for April, we accept that. I expect this debt to HMRC to be settled by us quickly - as I said we're talking to our stock market advisers."
Shaw claimed Preston were just one of several clubs given winding up orders, but said the other ones did not have to make an announcement as they are not publically-listed.
His confidence will do little to ease fears of supporters, given the club had to borrow £500,000 to pay wages and have a total debt of more than £12million.
Portsmouth have told goalkeeper David James he will be offered a contract to remain at the club next season.
James, 39, was part of England's 30-man provisional World Cup squad who flew to Austria on Monday to prepare for the tournament.
He is out-of-contract at the club, who finished bottom of the Premier League last season but administrator Andrew Andronikou hopes to convince him to stay at Fratton Park
"Two weeks ago we met with his agent, Colin Gordon, and said we wanted David to stay," he told The News.
"There are financial considerations, but we have informally made an offer to him and hopefully we'll move it on in the next few days."
Sheffield United have shown nine players the exit door with midfielder James Harper is the highest-profile casualty of the club's failure to secure even a play-off spot this term.
The former Reading man has been told he has no future at Bramall Lane alongside Glen Little, Henri Camara, Jonathon Fortune, Derek Geary, Justin Haber, Ian Bennett, Liban Abdi and Sam Wedgbury.
Cardiff City have been boosted by the return to training of Anthony Gerrard ahead of Sunday's Championship play-off final against Blackpool at Wembley.
The central defender has missed the last three games with a calf strain but is back in full training.
Kenny Jackett, the Millwall manager, is hoping to draw on the experience of last year's League One play-offs - where his side were beaten in the final by Scunthorpe - to help book a repeat trip to Wembley.
The Lions host Huddersfield Town in the second-leg of their semi-final on Tuesday night, and with the score at 0-0 will be favourites to progress to the final.
Jackett also know home advantage does not count for everything - they travelled to Leeds United last year and claimed a 1-1 draw to go through 2-1 on aggregate.
"I certainly hope in terms of experience and desire that we can put it to good use," he said, referring to last year's play-off games.
"But I really do believe that what wins football matches is good play. Huddersfield are a very good team. They've invested very heavily and we have a lot of respect for them. They have a lot of ability and have had a very good season as well."
Hull City's left-back Bernard Mendy, 28, has left the club by "mutual consent". The Tigers are seeking to cut back on wages following relegation from the Premier League.
Howard Wilkinson has been named interim chairman of Sheffield Wednesday following the resignation of Lee Strafford.
Strafford resigned following the apparent collapse of a takeover from an American consortium.
"It is a disappointment that the investment process has not resulted in a positive outcome having clearly been impacted by the relegation to League One," he said.
"Having said that, my view is that the club can progress without outside investment. For me, Wednesday can grow without external investment until such time as it needs to consolodiate its position back in the Premier League."
West Bromwich Albion have allowed Slovenia international midfielder Robert Koren to leave the club after deciding not to take up an option to retain his services following promotion to the Premier League.