"Today itself" is standard, correct English in South-Asian English, where attaching "itself" to a time or place word adds emphasis — "today itself" means "this very day." But to a US, UK, or Canadian native speaker, "itself" attached to "today" or "here" doesn't read as emphasis at all. It lands as a small grammatical slip and quietly marks the writer as non-native.
The emphasis you meant — "I'll do it as soon as today" — gets lost, because natives don't hear "this very day" in it. They keep the time phrase plain and, if they want emphasis, add it separately.
In a US/UK/Canadian workplace, just say "today." If you want to stress urgency, add it as its own beat: "today — actually, within the hour."
Drop the "itself" and let the plain time or place phrase carry the meaning:
Instead of
"I'll send it today itself."
Write
"I'll send it today."
Drops the "itself" that reads as non-native. If you want the emphasis, natives add it separately: "I'll send it today — actually, within the hour."
Instead of
"We finished it morning itself."
Write
"We finished it this morning."
Natives say "this morning," not "morning itself" — the time phrase already carries the meaning, so no intensifier is needed.
Instead of
"Let's meet here itself."
Write
"Let's meet right here."
"Right here" is how natives emphasize a place. "Here itself" sounds like a word-for-word translation of the emphasis.
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