The Sun claims the broadcaster is aiming to sign off the plans in the next few weeks. ITV was unavailable for comment this morning.
The extra show involves changing the contracts of judges Simon Cowell, Louis Walsh, Cheryl Cole and Dannii Minogue and paying them £25,000 each per extra programme.
The newspaper quoted a "show insider", who said: "ITV is struggling with cash so it reckons getting two X Factor shows a week will haul in the ads. And the fans will be able to watch their favourite acts again."
The show will be sponsored by Carphone Warehouse in the last year of a three-year deal.
The extra Sunday night shows will also help ITV fill a gap left in its scheduling by a recent cut to its drama budget that will mean one hour less of original programming per week.
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