Thanks for all the tips guys! I will check out each of the listed possibilities and will let you guys know the result.

One thing puzzles me is the fact that the noise is present during idling only and completely disappear on a slightest push on the accelerator.

So, can a bad bearing be one of the possible problems? is it highly?

When you guys talk about the dampener, is it the strut looking like thing( but smaller) located in front of the engine? below the valve cover level?