He had teamed up with the former Argentex CEO Harry Adams to make a possible bid for the firm.
The Argentex board had already rejected the approach made last month by the pair, as well as that from one other potential suitor.
It recommended a takeover proposal from IFX Payments, which has also provided a bridging loan to Argentex.
Argentex acts as a broker for non-speculative commercial currency transactions, helping clients to navigate currency risk exposure and access wholesale rates.
But the company was in a position last month where it urgently needed to raise cash to support its short-term liquidity position.
“Argentex has been exposed to significant volatility in foreign exchange rates, particularly in relation to the rapid devaluing of the US dollar against other major benchmark currencies which has been precipitated by the various recent announcements from US president Donald Trump regarding tariff policies and US government spending cuts,” it told investors last month.
That also saw trading in its shares suspended in London.
The next day, its predicament became more urgent, requiring an immediate cash injection to ensure the continued solvency of the group.
It subsequently secured a £10.5m bridging loan from IFX Payments. IFX subsequently provided a £20m revolving credit facility (RCF) for Argentex.
“The RCF enables Argentex to draw down funds to meet margin calls from its liquidity providers, in the event of further adverse foreign exchange movements,” the company noted.
Trading in its shares in the Alternative Investment Market also resumed earlier this month.
In a statement to investors, Argentex confirmed yesterday Mr Clune and Mr Adams no longer intend to make an offer for the firm.
Mr Clune founded Taxback.com in 1996.
In 2023, his CluneTech group sold its payroll software development unit, Immedis, to US multinational UKG in a €575m deal. He owned almost half of Immedis.
Mr Clune also has a 50pc stake in CluneTech’s TransferMate, a firm that facilitates crossborder payments for banks. It raised $70m in 2022, giving it a more than $1bn valuation.
Earlier this year, TransferMate became a payment service provider for Amazon.
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