Such a belief is clearly expressed in both Genesis and Leviticus.
But flesh with the life thereof, which is the blood thereof, shall ye
11 For the life of the flesh is in the blood: and I have given it to
you upon the altar to make an atonement for your souls: for it is the
blood that maketh an atonement for the soul.
12 Therefore I said unto the children of Israel, No soul of you shall
eat blood, neither shall any stranger that sojourneth among you eat
13 And whatsoever man there be of the children of Israel, or of the
strangers that sojourn among you, which hunteth and catcheth any beast
or fowl that may be eaten; he shall even pour out the blood thereof,
and cover it with dust.
14 For it is the life of all flesh; the blood of it is for the life
thereof: therefore I said unto the children of Israel, Ye shall eat
the blood of no manner of flesh: for the life of all flesh is the
blood thereof: whosoever eateth it shall be cut off.
In both cases, the blood-as-life theory is used specifically as the reason why eating blood should be forbidden.