You said you did not know him.
You said that you did not know him.
Apparently , while conversing , both are acceptable but while writing formally are they? Or is it the case that the two fall under two different structures? Like in the first one you did not know him is the noun clause to a transitive verb and the second one shows the transformation from direct speech to indirect speech and that way both are correct , is it? But noun clauses do require the conjunction that don't they ?