Concentration with no object?

I searched Bhikkhu Bodhi's translations of the Samyutta Nikaya, Angutarra Nikaya, and Majjima Nikaya, as well as Maurice Walsche's translation of the Dhiga Nikaya. The closest I could come to "incline your mind toward Nibbana" was advice from Sariputta to Anurudda, wherein the latter - who had achieved the jnanas was complaining to the former about encountering obstacles. Sariputta, in Bhikkhu Bodh's translation advises him to "direct your mind to the deathless element." In a different translation of the same text (by Nyanaponika Thera and Hellmuth Hec ker) Sariputta advises Anuruddha to "direct your mind to the deathless element, Nibbana." AN3:128 / AN3:130.

Since that's as close as I could come to your original quote, I'm afraid I can't be very helpful. However, withing the context of the exchange between Anuruddha and Sariputra, and your question concerning meditation without objects - especially in an Indo-Tibetan Mahayana context I can perhaps be of a little service.

Following Kamalasila, shamatha meditation can be undertaken with an external object, such as a pebble or statue; an internal object, such as the breath or a visualization; or it can be done without an object, in which case it is known as meditation on the essence of things (or shamatha without support). This last type of shamatha is a resting meditation and shouldn't be confused with vipasyana. Mingyur Rinpoche gives very clear, nice instructions in this technique, as does Thrangu Rinpoche and Dzogchen Ponlop Rinpoche.

On the other hand, it seems that Anuruddha had gained the jnanas of the form or formless realm. In classical Indian texts, one is advised to begin vipasyana prac tice after one has attained the meditative stability of the four formless realms. Various Tibetan teachers have suggested that one can begin sooner - some say as soon as one has achieved the fourth or fifth level of shamatha where the mind no longer strays from the object - no matter how long the meditation session. In any case, one needs strong meditative stability in order for vipasyana practice to be effective. Traditionally, vipasyana is divided into two parts; analyzing and resting. In the resting stage, one rests in one's realization or certainty, without engaging in further analysis or looking. One may subtly cling to a conceptualization of one's realization, but ideally, this is a sort of formless meditation. Similarly, in tantra mahamudra, one generates the image of a deity, and in the completion stage one dissolves the visualization and - ideally - rests in nonconceptual awareness. Both sutra mahamudra and Essence mahamudra also entail objectless meditation. All of which is to say that meditation without an object is indeed a part of the Mahayana path.

From Mahayana perspective true Nirvana is the non-abiding Nirvana, which is a state of not being bounded by any single interpretative framework whatsoever.

Does Master Gotama have any position at all?"

"A 'position,' Vaccha, is something that a Tathagata has done away with. - MN 72

So it's not as much a concentration without an object as it is without a reference point such as one delineating "better" (state) from "worse" (state).

Freedom from all frameworks is the inexpressible suchness or positive ambiguity where even the dichotomy of samsara/nirvana has been transcended.

As the sutta answers pointed out, attaining this freedom requires concentration to identify and stop the opposing factors, the factors of attachment/craving/aversion/non-suchness, through letting go and dispassion of wisdom.

It means the object is Nibbana and the mental attitudes leading to Nibbana, as literally said as follows:

And what is the faculty of concentration? There is the case where a monk, a disciple of the noble ones, making it his object to let go, attains concentration, attains singleness of mind.

SN 48.10

To whatever extent there are phenomena conditioned or unconditioned, dispassion is declared the foremost among them, that is, the crushing of pride, the removal of thirst, the uprooting of attachment, the termination of the round, the destruction of craving, dispassion, cessation, nibbāna. Those who have confidence in the Dhamma have confidence in the foremost, and for those who have confidence in the foremost, the result is foremost.

AN 4.34

Here, bhikkhus, a bhikkhu develops the mindfulness enlightenment factor, which is supported by seclusion, dispassion, and cessation, and ripens in relinquishment. He develops the investigation-of-states enlightenment factor…the energy enlightenment factor…the rapture enlightenment factor…the tranquillity enlightenment factor…the concentration enlightenment factor…the equanimity enlightenment factor, which is supported by seclusion, dispassion, and cessation, and ripens in relinquishment.

MN 118

Let's say you go to the doctor and get your blood pressure measured and it turns out to be high, probably because you were anxious at that moment. The doctor tells you to calm down, and then he will take another reading.

In order to do so, what would you concentrate on? Surely not on the blood pressure measurement device or the doctor. And surely not on nothing.

Your anxiety is due to clinging to some mental ideas related to the results of the measurement. In order to become calm, you need to let go of that clinging.

Similarly, to incline your mind towards Nibbana, to extinguish suffering, you need to let go of your craving and clinging, which is only possible by the cultivation of wisdom and uprooting of ignorance, as explained by the analogy of the South Indian monkey trap.