Analysis

If your sentence was "There is nothing to say" I would translate into

Il n’y a rien à dire

But you asked for "talk about" which should be translated into "discuter de".
But the sentence is about not "talk about" so, no discussion => no need to talk => rien à dire.

Answer

So, if we know what we are talking about, I would use :

Il n’y a rien à en dire.

We use "en" to express this is true only about a particular subject.

Alternative answer

or if it’s "There is nothing to talk about blahblah"

Il n’y a rien à dire à propos de …

Il n’y a rien duquel on doit parler

sounds wrong, I think it should be

Il n’y a rien dont on doit parler

(not sure about the actual grammar rule here, feel free to edit)

which could work, with a slight difference: there may be something to say, but it’s not worth being said.

Also, it really depends on the situation.

Litteraly, a traduction for your two sentence will be the answer of Yohan, it’s a factual answer. But you may need to precise about what.

Il n’y a rien à dire là dessus. => There is nothing to say on this topic.

If you want to close the discussion, you can also say

Il n’y a rien à ajouter, la discussion est close.

If you want to signify someone you have nothing to discuss with him. (Can be rude)

Nous n’avons rien à nous dire. => We have nothing to discuss/talk about.

But if you need an accurate answer, you should add the context for each phrase.

"There is nothing to talk about"

Usually this implies a topic, such as in "There is nothing to talk about this book". In French, we’d prefer to explicitly say what is the topic:

Il n’y a rien à dire sur ce livre.

"Il n’y a rien à dire" feels rather weak in this context. Maybe "Il n’y a rien à en dire", just like @YohannV. said is acceptable, but really feels weak. Usually to insist that there is nothing to talk about, you name that thing. It can even be done like this: "Ce livre, il n’y a rien à en dire."

People who really want to be heard will even say out loud "Il n’y a rien à dire" before saying, very slightly toned down "sur ce livre". The subtlety here is perceptible for native French-speakers.

But as a rule and unless it’s really personal (such as emotions), you name the context.

"There is nothing to discuss"

Il n’y a pas matière à discussion.

Il n’y a pas de matière à discussion.

This clearly means that the discussion will lead nowhere and it’s a very strong indicator that unless a very fundamental change happens in the topic, this topic shouldn’t be brought again. Both forms are accepted and the first might be preferred. Depending on the tone, it can be very polite or very firm.

The following suggestions are far from literal translations and lack the finality expressed in the blunt declarations you seek to translate, but in the right context I think you could use “A quoi bon” (from Reverso) to convey a similar message (i.e., that a discussion will serve no purpose) by instead “asking” (first in English):
“What’s the point/use/good/ of [further] discussion/discussing [it]///talking about it”,
which could lead in French to:

“A quoi bon [en]
discuter?
(“… cela voudrait dire que ce que l’on vise au travers de la
discussion, l’idéal rêvé, n’est pas réalisable, que l’idéal de
discussion qu’on s’efforçait de construire n’est pas atteignable.”
from Devoir de philosophie)

and

A quoi bon en
parler?
(usage example from Soyez bienveillant avec vous-même ! Libérez vos
émotions! by Bertrand CANAVY where the subject (breathing) is deemed
to be so natural and banal that we don’t think about it or study it,
so “A quoi bon en parler”?

(Here’s a YouTube video where you can hear/see Emmanuel Moire’s three entertaining uses of “A quoi bon” (with “résister”, “hésiter”, and “s’éviter”) in his very nice song Adulte & Sexy.)