No. The reason it's happening is that Earth's rotation is faster than the Moon's orbit - a day is shorter than a month.

Because of this, the Moon is leeching kinetic energy from Earth's rotation to orbit faster (drifting further away is simply a consequence of orbiting faster). This speeds up the Moon's orbit at the cost of slowing the Earth's rotation. Over time this energy-leeching will stabilize once the Moon has sped up so much, and the Earth has slowed down so much, that the Moon's orbit and the Earth's rotation will take the exact same amount of time - a day will be equal to a month - and the Moon will appear motionless in the sky. This is called tidal locking.

But as other comments have stated, this process will take so long that the Sun will kill us all long before it finishes.