The newswire has reported that Oberthur, which launch a hostile takeover bid for De La Rue in December 2010, would fulfil the print element of the £1bn, 10-year contract, while G4S would provide cash handling and security services.
G4S, which is the world's largest security firm, was heavily criticised for failing to deliver on its contract to provide security for the London 2012 Olympic Games, leading to members of the UK Armed Forces being called in at the last minute to plug the gap and costing the firm £50m.
Following the Olympics fiasco, G4S announced that it would not be bidding for sporting contracts including the FIFA 2014 World Cup in Brazil.
However, the firm was back in the public spotlight in August when it was forced to withdraw its bid for the £150m contract to monitor criminals electronically after it emerged that both it and rival Serco had received payments for tagging criminals who had either died or been sent back to prison.
The Bank of England's £1bn banknote contract, which is likely to include a new generation of polymer banknotes, is due to commence in April 2015.
De La Rue, which has held the contract to supply currency to the Bank of England since 2003, is understood to be rebidding for the contract. Other bidders are thought to include German firm Giesecke & Devrient, Canada-based Fortress Paper's banknote division Landqart and UK-based Innovia Security.
Oberthur and G4S were unavailable for comment.
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