I was surfing on the internet, and I have encountered rumours that in the 5th edition of DnD in Forgotten Realms world, the Old Deities will come back (Bhaal, Myrkul, Leira etc.) What is more, I have heard that Bhaal is confirmed.
Is this true, and are there any official sources that confirm this?
Yes, the old deities are really coming back. Along with the list of old deities in the Forgotten Realms section of the gods listed in the updated basic rules, (and the gods listed amongst many pantheons in the Player's Handbook) there is also the "Sundering" story line. The Player's Handbook lists 39 deities for the Forgotten Realms setting with their domains and symbols. And 24 "non-human deities" which are shared between Greyhawk and Forgotten Realms.
During the Sundering the worlds of Toril and Abeir (which were united during the Era of Upheaval) are being separated from each other. During this time, the various gods are creating "chosen" mortals who are intended to bring power to the gods, in the hope that when "things are settled" these gods will have the power required to remain a god. There seems to be confusion amongst the gods as to what Ao actually has in mind as he re-writes things.
Noted events during the Sundering are the diminishing of Spellplague effects, magic changing its nature to the way it worked in the past, such that old spellbooks work and recent ones do not. "The Weave" has new prominence, and most importantly for this question, various gods are found to either not be dead, to be re-united, or to be recreated through various events. It seems that in the various divine schemes to "get enough followers" all divine who have a "chosen", get chosen to remain a god, in a fun twist of the meaning of the "chosen".
The three deities you reference (Bhaal, Myrkul, and Leira) are listed in Appendix B of the 5E Players Handbook (p. 294).
Version 0.2 of the Basic rules includes a list of Forgotten Realms deities, and it looks like most of the old deities have returned, including some that died before 3e was even released. Bhaal, Leira, and Mrykul -the three you mention in your question- are all back on the list. So are Azuth, Mystra, and Savras, and most of the other popular formerly-dead deities. However, there are a few entities who haven't been mentioned yet that one might have expected to see, such as Xvim and Asmodeus.
Nonhuman pantheons are not part of the "big" list, though they do get a brief mention in that section. The Dwarven pantheon, at least, appears to all be back: all the old names are listed, but stats aren't given. The same likely holds for other races. Animal deities, like Nobanion and Lurue, also aren't listed.
In any event, the Basic rules don't give any history or other reasons for why this happened. The PHB and DMG might explain further, or this could be relegated to the novels.
Not only are some of the old gods coming back but it also seems that the "aspects" are gone, meaning that all the deities that were merged in 4e (like Talos being an aspect of Gruumsh) are back to being separate entities.
The only canon list from 5e Forgotten Realms is in the Sword Coast Adventure's Guide.
Apparently the concept of Greater/Lesser deity has also disappeared.
