The Glasgow club, which has previously said it was debt free, responded to the latest embarrassing episode to befall the brand by saying the sums sought were insignificant, and that it was close to an agreement over payment.
The claim is understood to have arisen from a failure to pay two of four invoices issued by Orlit Enterprises.
It is believed to have arisen from the Singapore company's involvement in introducing investors to provide seed capital to buy Rangers from the administrators and secure the June 2012 payroll.
Orlit Enterprises is said to have taken the action because there was no satisfactory answer to the non-payment, and is understood to be seeking the winding-up of The Rangers Football Club Limited (RFCL), formerly Sevco Scotland Ltd, the company vehicle used to buy the Ibrox club's assets while in administration.
The club said in a statement: "With regard to stories circulating about Rangers and Orlit, the sums sought are insignificant and an agreement has been reached subject to the necessary paperwork.
"Rangers Football Club is capable of meeting any debts presented legitimately and we would like to stress to our supporters there is no threat to the club whatsoever. The matter is unworthy of further comment."
Orlit is linked to businessman Chan Fook Meng, an associate of Rangers chief executive Charles Green.
In its offer to float RFCL's parent company Rangers International Football Club plc on the AIM market of the London Stock Exchange, the club stated it did not have access to banking facilities.
Mr Green has consistently claimed Rangers is "debt-free" and the share prospectus stated that, as of October 31, "RFCL has no debt".
The club subsequently announced it had raised more than £22 million from its listing.
Mr Green stated he had secured £17m in pledges from institutional investors – including Legal & General, Hargreaves Hale and Artemis – and set aside £10m for fans to buy a stake.
Oldco Rangers entered administration on February 14, 2012, nine months after Craig Whyte bought Sir David Murray's 85.6% shareholding for £1.
HMRC filed a petition at the Court of Session in Edinburgh for a court-appointed administrator over an unpaid tax bill of £14m incurred since Whyte took over at Ibrox.
But the court agreed to the withdrawal of the HMRC petition to allow Whyte to appoint his own administrators, Duff and Phelps.
The administrators negotiated a sale of the club's assets to a consortium led by Mr Green, the former Sheffield United chairman for £5.5m. The team now plies its trade in the Scottish Third Division.
Meanwhile Rangers Oldco is in the process of being liquidated after Lord Hodge appointed accountancy and audit firm BDO as interim liquidators in November after eight months in administration.
BDO is currently investigating the books to determine whether further repayment can be made to creditors, and to pursue any outstanding debts.
Orlit Enterprises was unavailable for comment.
Mr Green was formerly a non-executive director of Mongolian mining firm Nova Resources – until his resignation "to pursue other interests" – when Chan Fook Meng was its chief executive.
Rangers financial director Brian Stockbridge has acted as an adviser and broker for companies associated with Mr Chan.
On Monday HMRC lodged an appeal against a tax tribunal finding in favour of Rangers' past use of Employee Benefit Trusts (EBTs).
HMRC claimed the scheme, which was used from 2001 to 2010 to make £47.65m in payments to players and staff in the form of tax-free loans, was illegal.
But the Rangers directors disputed this and a First Tier Tax Tribunal ruled the scheme did not breach tax law. The case is now be heard at an Upper Tier Tax Tribunal.