Thew use of "like" in your second alternative is very informal, and technically incorrect. I advise against using it unless there is a deliberate intention to imitate the speech of particular subgroups where that usage was common, particularly the youth of the 1970s and 1980s.
The first alternative:
Did ABC tell XYZ "I don't need it today. Bring it tomorrow"?
is acceptable, although I would prefer a comma or a colon after "XYZ" as
Did ABC tell XYZ: "I don't need it today. Bring it tomorrow"?
If the intent is to indicate that the quotation may not be exact, one could write:
Did ABC tell XYZ something like: "I don't need it today. Bring it tomorrow"?
Did ABC tell XYZ something similar to "I don't need it today. Bring it tomorrow"?
One couyld also reword with indirect dialog, not using quote3s. For example:
Did ABC tell XYZ that it wasn't needed today, and should be brought tomorrow instead?
There are many valid ways to rephrase this, changing emphasis slightly but not really altering the meaning.