The El Mundo report said Mr Rajoy had sent words of support to Luis Barcenas, former treasurer of the governing Popular Party (PP).
Mr Barcenas is in custody facing trial for corruption and tax fraud. He denies the allegations.
Mr Rajoy, too, denies any wrongdoing.
The PP's former treasurer was due to appear before a judge at the Audiencia Nacional - Spain's national criminal court - on Monday, a week after he admitted for the first time that handwriting in a ledger detailing payments belonged to him.
A series of newspaper allegations that Mr Rajoy and other top politicians received illicit payments has enraged a country in the depths of recession and record unemployment.
It is claimed that Mr Barcenas ran a PP slush fund that took donations from construction magnates and distributed them to party leaders in cash.
El Mundo newspaper said last week it had delivered documents with Mr Barcenas's original ledger entries to the national criminal court.
Another Spanish paper, El Pais, published similar documents earlier this year.
The prime minister is expected to face questions about the scandal from reporters when he gives a news conference with visiting Polish PM Donald Tusk on Monday.
The leader of the country's main opposition Socialist Party, Alfredo Perez Rubalcaba, called for Mr Rajoy's immediate resignation on Sunday "given the unsustainable political situation in Spain".
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