The Knight-Hennessy Scholars program follows the practices of your graduate degree program: if your graduate degree program does not require standardized tests, then neither does the Knight-Hennessy Scholars program. Any required test scores are due to the Knight-Hennessy Scholars program by your graduate degree program's application deadline or the Knight-Hennessy Scholars program's application deadline, whichever is later. If your testing date is after the October 10 Knight-Hennessy Scholars deadline, then you simply leave that section of the application blank and provide the scores from your application status page (which you can access only after submitting your application). For the GRE, your unofficial scores (i.e., the quantitative and verbal scores you receive immediately upon taking the test) will suffice for the Knight-Hennessy Scholars program.
You must be fluent in English — listening, reading, speaking, and writing — to study at Stanford. If you earned or expect to earn a degree from a university where English is the official and sole language of instruction, then you do not need results of an English proficiency exam. Otherwise, you do. Your citizenship, residence, and/or work experience do not exempt you from this requirement.
All Stanford graduate degree programs accept the TOEFL. The minimum TOEFL score for most graduate programs at Stanford is 100iBT or 600PBT. Some departments only accept scores obtained within the last 18 months, while others accept scores for 24 months. The MBA Program is the only Stanford graduate program that also accepts the IELTS and PTE. You may read more about this policy on the Graduate Admissions website (TOEFL) or MBA Admissions Office website (TOEFL, IELTS, or PTE).