Sort of (but not really)
The rebirth of Emperor has been first described as possible in the "Realm of Chaos: Lost and the Damned". There is the (already mentioned) theory of the Star Child and the Sensei, guarded by the Illuminati:
As the spirit of the Emperor drifted through the warp, it gradually dissolved into the flow of energy, returning to the cosmic force of the nature of the warp in its uncorrupted form. Only a tiny core of the Emperor's humanity remained whole, like a small child bobbing upon the tide of a colossal storm in a tiny reed boar.[...] For just as the New Man had been born from the collective souls of the shamans of old, so the Emperor's soul might be reborn one day. But that day would lie far in the future when the cries for a new saviour would strengthen the core of the Emperor's soul and rekindle it into a new life.
Meanwhile the soul of the Emperor was a merely a potential, a child awaiting birth, the Star Child.
Sensei are the true children of Emperor:
The Star Child also has his Champions, known as the Sensei. Although they do not necessarily know their true identity, these people are actually descended from the Emperor's own descendants and their genetic structure is similar to his.[...] Although they can be killed hey do not age and possess amazing powers of recovery. They radiate natural confidence and harmony, and can even draw upon the energies of war to use their psychic powers [...] without attracting demons or other malicious psychic forces.
Information about those two is guarded by the mysterious organisation known as Illuminati:
The Illuminati are a secret society, existing beyond even the Emperor's knowledge, but manipulating and interpreting the Imperial Will to bring about their objectives.Every member is a part of the society by virtue of being "illuminated" through the experience of daemonic possession, and finally salvation. Possessed by a daemon, they have done what seems impossible, exorcising the daemon from their body through their own sheer will.[...] The Illuminati influence events to pave the way for the Emperor's rebirth, and gather together the Sensei, protecting them from the persecution of the Inquisition.
Although their plans regarding Sensei are not so benevolent:
The Illuminati plan to rejuvenate the Emperor by sacrificing His descendants, the Sensei, at the moment the Emperor's will finally fails. The Emperor will be reborn, as the Sensei-Emperor, to again lead humanity directly. Their plans are a carefully kept secret; should the Emperor learn their plan, He may see no reason to continue to endure, and allow Himself to die prematurely. Should the Sensei learn, they may be unwilling to meet their intended fate.
Now, the information regarding Illuminati has been shown in at least one book: "The Inquisition War" by Ian Watson, so it is a concept that is in theory still within the 40k universe, although since its publication in 2004 there was no further information about this group in any other books, although 1d4chan mentions that:
In the third edition, as part of general grimdarkification and realizing that the whole Star Child thing made about as much sense as Space Marines being all beakie space cops, Games Workshop said that the Inquisition had decided that they were actually a Tzeentchian cult that plotted to kill the Emperor and plunge the Imperium into Chaos. They have since been eradicated entirely.
In short, they were long since retconned and are unlikely to be making any further appearances.
What is NOW a canon is the information that the Golden Throne is failing and it is Mechanicus doesn't know how to fix it, as described in the 5th edition of the Warhammer 40,000 5th Edition Rulebook
It has been mentioned as possible once, since then has been retconned and now all we know is that Emperor will die soon-ish (unless he won't)