The two missing people were Spaniards named Victor and José, said national disaster agency spokesman Sutopo Purwo Nugroho in a tweet on Monday.
Spain's foreign ministry was unable to confirm this with The Local but said it was working closely with Indonesian authorities to establish whether the missing pair were indeed Spaniards.
The ministry did state, however, that the two Spanish tourists who has been rescued after the shipwreck were safe and sound.
It was one of those survivors who initially informed authorities that they had met another Spanish couple on board.
Rafael Martínez, one of the survivors, told Spanish daily ABC how they managed to overcome cold, hunger, cramps, exhaustion and jellyfish before being rescued.
The vessel was carrying 25 people between the Indonesian islands of Lombok and Komodo, famous for its giant lizard species – the Komodo dragon.
Fifteen out of the 25 passengers on board were tourists from Germany, England, New Zealand, Holland, France and Spain. The other ten were Indonesian citizens.
According to Spanish news agency EFE, bad weather may have caused the boat to hit a reef and spring a leak.
Thirteen of the 25 passengers were lost at sea for several hours before being rescued on Monday.
One French survivor told news agency AFP on Sunday that he and other survivor swam for six hours before making shore on the volcanic island of Sangeang. They survived by eating leaves and drinking urine, he added.