Majority of you might know the three bodies doctrine in Indian philosophies, i.e., Gross body, subtle body and casual body. We can see gross body with our two eyes. But is it possible to see subtle body?
I thought you are asking if scriptures mention whether it is possible to see the subtle body or not.
So, if you are also looking for answers like this, then Sri Ramakrishna also saw his own subtle body coming out of his gross body. This inicident is quite famous in his life. He saw signs of the throat disease in that subtle body that he were to be afflicted with in the future.
This is an indication of the fact that diseases affect the subtle body much before they affect the gross body.
So, if we are being able to devise some methods of diagnosing diseases at the subtle level then we will be far better equipped to fight against them than we are right now.
While at Shyampukur Sri Ramakrishna one day had a vision of his subtle body emerging from the gross sheath and moving about the room. It had a number of sores on the back. He was puzzled by the sight, but it was made clear to him that the touch of profane people had caused those sores on the body. They themselves had been purified, but they had left the suffering arising from their own sins with him. When he described this vision to his devotees, Narendra and some others observed that the Master’s vision was in conformity with the doctrine of vicarious atonement postulated in certain religions like Christianity and Vaishnavism. More than two months passed, but there was no sign of improvement. On the contrary the condition of the Master was gradually going from bad to worse. When treatment proved ineffectual, Dr. Sarkar advised a change to some garden-house outside the city. Accordingly the spacious gardenhouse of Gopal Chandra Ghosh at Cossipore was hired. In the afternoon of the 11th of December 1885, Sri Ramakrishna was removed to the new premises.
This is quoted from "A SHORT LIFE OF SRI RAMAKRISHNA" by Swami Tejasananda.. (Go to page 100 of the PDF).
Sri Ramakrishna once said that he saw the subtle body of his nephew named Akshay come out of the body like a sword out of its scabbard.
During this period Sri Ramakrishna suffered several bereavements. The first was the death of a nephew named Akshay. After the young man's death Sri Ramakrishna said: "Akshay died before my very eyes. But it did not affect me in the least. I stood by and watched a man die. It was like a sword being drawn from its scabbard. I enjoyed the scene, and laughed and sang and danced over it. They removed the body and cremated it. But the next day as I stood there (pointing to the southeast verandah of his room), I felt a racking pain for the loss of Akshay, as if somebody were squeezing my heart like a wet towel. I wondered at it and thought that the Mother was teaching me a lesson. I was not much concerned even with my own body — much less with a relative. But if such was my pain at the loss of a nephew, how much more must be the grief of the householders at the loss of their near and dear ones!"
The Gospel of Sri Ramakrishna, Introduction, Summary of the Master's Spiritual Experiences, translated by Swami Nikhilananda
Yes, we can see the subtle body but for that you need to use your third eye and for that you need yoga, deep meditation and follow some other rules and regulations, strictly. Read the following answer by given by Sri Chinmoy :
We have three bodies: the gross physical, the subtle and the causal. From the causal, the creation starts, and in the broadest sense we call it AUM, the cosmic AUM. Then comes the subtle body. You don't see the subtle body with your gross physical eyes; you need the third eye, or inner eye, to see it. When the seven major centres in the being open up, you can see the subtle body. You think that you are using your two ordinary eyes, but the vision that you are using is coming from the inner eye, which can see everything-even on the gross physical plane. It is not that only when you keep your eyes closed, you will be able to see with the inner eye. Even when the ordinary eyes are wide open, the inner vision, or the third eye, can perform its duty.