My friend asks me: When are you leaving? I say: I leave Monday early morning. Or

[B45]

My friend asks me: When are you leaving?

I say: I leave Monday early morning. Or I leave Monday early in the morning.

Are both okay here?

 

[SoothingDave]

"Early Monday morning" is most natural. "Monday early in the morning" is OK. "Monday early morning" is awkward.

 

[Roman55]

I am not a teacher.

If you're saying it I'd stress Monday and leave a short pause after it. In writing you would need a comma for that. They would both be OK like that, but I would probably say, 'I leave/I'm leaving early Monday morning.'