Craig Stevenson, owner of Braehead Foods, was quoted as saying a winding-up petition was on its way to Rugby Park over a £16,000 bill for supplies to the club's Park Hotel. However, Johnston insisted that the debt was being dealt with in the usual manner and there was no danger to the club, who have a debt of close to £10million.
Johnston said: "There is no winding-up petition. We are dealing with commercial creditors in the way we always do.
"This creditor is obviously looking to get some priority for payment for himself and it's unfortunate that he has decided to take it into the public domain. If we did that to the people who owe the football club money there would be a bit of an outcry.
"It's clear from his own comments that we're not talking about a large amount of money, relatively speaking, and that we are not talking about a particularly aged debt. The bulk of the debt he is claiming isn't due for payment until the end of January, as far as we are concerned."
Stevenson told the Daily Mail he believed a legal letter was on its way to Johnston and that sheriff officers could serve a winding-up petition to the club on Monday.
Johnston, who will chair the club's AGM on Thursday, said: "We had an email from solicitors late on Friday afternoon which I will be responding to on Monday morning but nothing beyond an email.
"It's a relatively small amount he is seeking but there are various procedures we need to go through before paying creditors, such as stock audits. We are awaiting the outcome of that before making payment.
"I'm a solicitor and I have met many sheriff officers so the idea of getting a visit from them doesn't cause many concerns, but it creates bad publicity and uncertainty for supporters and other suppliers.
"I can reassure supporters there is no truth in the suggestion that a winding-up petition is on its way. It's business as usual." Johnston added: "At the end of December wages for all staff were up to date, all the tax payments were up to date."