These days is a common idiom. We use those days literally, not idiomatically.
These days refers to the present. Those days refers to the past: Those days are long gone.
The second (indirect) version depends on context:
- If he said it recently and it applies to the present, then these days is correct.
- If the time it refers to is in the past, then those days cannot replace the idiom these days. (Although it would be convenient!) You could say "in those days" or "back then."