1. Recall what Nessler's reagent is

   Nessler's reagent is an alkaline solution of potassium tetraiodomercurate(II).

2. Write the complex ion present

   The tetraiodomercurate(II) ion is: $[\mathrm{HgI}_4]^{2-}$

3. Balance the charge with potassium ions

   Since the complex ion has charge $-2$, it requires $2$ potassium ions: $\mathrm{K}_2[\mathrm{HgI}_4]$

   This is written as: $\mathrm{K}_2\mathrm{HgI}_4$

4. Check the options

   • A: $\mathrm{KHgI}_3$ — not the standard formula of Nessler's reagent.
   • B: $\mathrm{HgI}_2$ — this is mercuric iodide, not Nessler's reagent.
   • C: $\mathrm{KHg}_2\mathrm{I}_2$ — incorrect formula.
   • D: $\mathrm{K}_2\mathrm{HgI}_4$ — correct.

5. Final answer

   Nessler's reagent is: $\boxed{\mathrm{K}_2\mathrm{HgI}_4}$

So, the correct option is D.