Irregularities in the transfer paperwork mean the youngster is ineligible for official matches, and the Brazilians are considering going to Fifa in order to make him available
The starlet, 22, finalised a move to Vila Belmiro in July 2012, signing a four-year contract with the Peixe in a transfer worth $2 million for 50 per cent of his playing rights from the Argentines.
Having announced the move over two weeks ago, 'Pato' was expected to be handed a first start this Sunday, away to Nautico.
According to Globoesporte, however, Independiente have failed to hand Rodriguez's registration details to the Argentine Football Association (AFA), who in turn have been unable to officialise the transfer with Fifa.
This means that the youngster, who has been training with the Peixe reserves, is still ineligible to play competitive football with his new team.
Santos will consider making an official complaint to the world football governing body, pressuring Independiente into completing the paperwork, which will allow their new signing to take to the field.
Having been hit with the absences of key players such as Neymar and Ganso due to London 2012, Santos languish in 16th place in the table - just one point clear of the relegation zone.