Is nirvana a conceptual construction?

Nirvana or Nibbana is not a thought or concept of the mind. It is that which is experienced by the mind, when it is completely free of all fetters and defilements.

I quote from this answer below. Please see that answer for a detailed analysis including sutta quotes.

So, Nibbana is not a thought of the mind, not a concept of the mind, not a state of the mind, not a state of consciousness and also not a feeling. However, when the mind experiences this Nibbana, which is not conditioned, not compounded, not suffering, not impermanent, not arising, not ceasing and not changing, it experiences bliss. The mind can therefore experience Nibbana, but it cannot feel it or think about it.

Sukha or happiness for an unenlightened person is experienced when encountering pleasant feelings (from the six senses) or when encountering the cessation of painful feelings (from the six senses). But for an arahat, sukha or bliss (in this context) is experienced when encountering neutral feelings, no feelings and Nibbana.

Also from that answer:
From AN 9.34 (translated by Bhikkhu Sujato):

Ven: Sariputta: “Reverends, extinguishment (Nibbana) is bliss!

Ven. Udayi: “But Reverend Sāriputta, what’s blissful about it, since nothing is felt?”

Ven. Sariputta: “The fact that nothing is felt is precisely what’s blissful about it.

Obviously people have conceptions about it (and those conceptions are conceptual constructions).

I think that nibbana itself is defined as unconstructed -- or unconditioned -- or more literally, "undefiled", "extinguished", etc., are among its many attributes.

I think the idea is that because it isn't constructed, it is therefore not subject to decay and coming apart -- according to the "three characteristics", it's "sankharas" (i.e. constructed things) which are impermanent ... and nibbana isn't a sankhara.

I'm using "conditioned" and "constructed" here as synonyms, which perhaps isn't quite right, but I think it's along the right lines -- see also this answer (which says that the non-construction of something may depend on some condition, but that what's unconstructed isn't itself impermanent).

This is a good question. I have not experienced anything close to Nirvana. But from what Buddha has said we can understand it as a natural state of unborn , uncreate and as a state of unbecoming. It is grasped conceptually but once nirvana is achieved you don’t need to hold on to any concept. It is a natural state of unborn existence...

Are you asking about the referent of the word "nirvana"?

The referent of the word nirvana is a concept of nirvana, and the referent of that concept is ... WHAT?

The referent of that concept is the actual experiential liberation of the mind.

Liberation from what? Liberation from the confines of concepts and therefore from the dukkha that comes from the clash between concepts, or between the concepts on one hand and the ontological reality on the other.

Now you tell me, is this Liberation a conceptual construct? For you perhaps it is, because you are asking about it? For me - not anymore, because I attained it in practice.

Once attained, the concept of nirvana has no referent. One does not engage in semiotic games anymore. No bullshit like "nirvana" and "liberation".

Some aspects of Nagarjuna’s Madhyamaka-karika could suggest that, but that is not the “orthodox” Madhyamika stance, at least amongst Tibetans

When language is involved, everything becomes a conceptual construct. That's the problem with language, you have to create a concept of something to explain something. The question in itself is unclear, but Nirvana is a goal, or a state. It's a state of freedom from suffering and rebirth. When you reach nirvana, your mind is free from the 3 fires. The fires of ignorance/delusion, attatchment/greed and aversion/hate. You do not experience rebirth anymore, as you have removed the attachment to life.

Is nirvana a conceptual construction? For any / only some Buddhists

Of course it'd depend on who you ask. To a deep-sea fish, the fresh breeze of the open sky will remain a conceptual construction, but to a man on land, that's something possible to have first-hand experience of. Similarly, Nibbana will remain a conceptual construction until one's attained awakening like the Buddha and His noble disciples.