Sky News has learnt that a number of institutions have been arguing for Mr Rothschild, who has led a successful turnaround of the listed industrials group Volex, to be appointed as Kevin Loosemore's successor.

City sources confirmed on Wednesday that De La Rue, whose customers include the Bank of England, had held discussions in recent weeks with the scion of the eponymous banking dynasty.

However, it was unclear whether he had decided to withdraw from the recruitment process.

Mr Rothschild became a prominent and at times controversial figure in the City after he floated two vehicles which went on to acquire overseas natural resources companies.

Under his stewardship, however, shares in Volex have multiplied more than threefold, and the company now has a market value of well over £400m.

Other contenders for the role are said to include Clive Whiley, the Mothercare chairman, while Paul Forman, former chief executive of the filters manufacturer Essentra, is also understood to have been approached.

The search for a new chairman was precipitated by a threat from Crystal Amber, one of De La Rue's biggest investors, to seek Mr Loosemore's ousting by requisitioning an extraordinary general meeting last month.

Crystal Amber nominated Pepijn Dinandt, an industrialist, as his successor, although a person close to the banknote printer said he was unlikely to get the job.

Earlier this month, De La Rue issued a statement to say it had begun interviewing prospective candidates, describing it as "a fast-track process, supported by a search firm".

"Interviews have taken place with a range of candidates who have come forward with the support of shareholders and partners, as well as from search activities," it told the stock exchange.

"We are not yet at the stage of making a final appointment but are progressing candidates through the final stage of our process.

"These candidates have strong backgrounds in relevant situations."

De La Rue has performed appallingly in recent years, issuing a string of profit warnings, encountering operational problems in a number of key international markets, and paying its top executives packages which have faced heavy criticism from investors.

Many shareholders believe De La Rue is vulnerable to a low-ball takeover offer, with the likes of American rival Crane NXT frequently touted as a potential bidder.

The London-listed company has seen its shares slump by two-thirds over the last year, and now has a market value of just £80m.

It raised £100m from a share sale in July 2020.

Last month, Sky News revealed that De La Rue had requested breathing space from its pension trustees by delaying nearly £20m of retirement funding payments.

Controversially, it also criticised its auditor, EY, for including a going concern warning in its accounts.

A spokesman for De La Rue did not respond to a request for comment, while Mr Rothschild could not be reached for comment.