The Spanish government is expected to revise the country's 2016 state budget should Parliament decide to support the agreement, according to the news outlet.
In July, Rajoy said Spain would contribute 11 to 12 percent of the total bailout budget once the final agreement was approved.
Earlier in the day, Annika Breidthardt, the spokeswoman for the European Commission, said that Athens and its international creditors had reached a technical but not political agreement on the new bailout deal for Greece.
According to her, the deal is expected to be concluded by August 20.
The third bailout package amounting to some $95 billion will be administered to Greece by its international lenders over the next three years in exchange for austerity reforms. The country's last bailout program expired on June 30.
Greece owes more than $270 billion to the International Monetary Fund, the European Central Bank and eurozone nations.
