Four Spanish political groups are demanding that Rajoy answer questions about the scandal in Parliament.
The opposition socialist PSOE party, the left-wing IU party, the Catalan Convergence and Union (CiU) party, and a group of non-aligned members of parliament have all presented petitions calling for Rajoy to answer questions about the slush fund allegations.
The scandal implicating Rajoy reignited on Tuesday with the publication of an original handwritten account ledger in Spain's El Mundo newspaper allegedly showing illegal payments to the Spanish leader when he was a minister in the 1980s.
The paper said the ledgers were compiled in part by the party's imprisoned former treasurer Luis Bárcenas, who is now behind bars facing corruption charges.
But Rajoy looks set to avoid an appearance in Parliament as the ruling Popular Party has an absolute parliamentary majority and can therefore avoid a vote which would oblige the Spanish leader to answer questions from the floor.
The Popular Party has distanced itself from Bárcenas and has said it has no fear of possible revelations by him from his prison cell.
Bárcenas is currently in jail for his role in another corruption scandal linking a group of Spanish businessmen with the Popular Party.
On Monday, Spanish High Court judge Pablo Ruz said Bárcenas would be called to answer questions about the slush fund.
The judge also cited El Mundo director Pedro J. Ramírez to appear as a witness in the case.