On paper only, if the drawings are still around.
Nothing in a format that can get fed into a computer...:^)
If they’ve got an old photograph, why don’t they just feed it into a 3D printer? They will have a new Titanic in no time (as long as they don’t run out of ink). And, since the photos back then were just Black & White, they’ll only have to paint the ship to be ready! :)
Actually, they can.
Not directly, but the process has been available for decades, and it can be accomplished in one tenth the time and manpower as the originals and, simultaneously produce modern manufacturing computer input for fabrication.
I would hope the "near identical" refers only to visible appearance, inside and out; it does NOT mean inferior metals, inferior propulsion and lack of modern stability controls.
A double hull, ultra-strong modern steels, better compartmentalization and safety systems are presumed to be incorporated, as well as all modern navigation equipment.