NOT A TEACHER
I'm not 100% sure, but I believe that both can be used interchangeably.
The Longman Dictionary of Contemporary English lists both, so I think both are correct.
ˈno one S1 W2 , no-one pronoun
not anyone SYN nobody : No one likes being criticized.
Thereís no one else I really want to invite apart from you.
Has no one phoned about the car?
No one can say I didnít warn you.
no one, nobody Do not use another negative word (eg 'not') with no one and nobody :
Nobody could hear me (NOT Nobody could not hear me).
No one did anything about the problem (NOT No one did nothing ...).
Do not use 'of' after no one and nobody . Use none of or, if you are talking about two people, neither of :
None of them saw him.
Neither of his parents had come to the wedding.
Student or Learner