The Qualifications and Curriculum Authority has urged heads to verify that they have all their test papers. Heads have also been asked to find out if their English, maths and science teachers have been offered copies of the tests, which are due to start next week.
The QCA is investigating reports in the Daily Mirror that copies of English and maths papers had been offered to a member of the public in Manchester for pound;100.
The QCA said: "We have launched a thorough investigation and have referred the matter to the police. The QCA will ensure that the tests are not compromised and we have contingency plans."
Among these contingencies are the withdrawal of the test papers, which the QCA was considering as The TES went to press. Reserve tests have already been drawn up.
Around 600,000 pupils are due to start sitting KS3 tests on Tuesday.