Usually, the expression is: out of the corner of his eye (not eyes)
"I was watching TV when out of the corner of my eye I saw something moving near the door."
(The TV is in front of me and the door is over to my right.)
Normally, we look forwards. We can see what is in front of us very clearly. We can also see what is to the side of us, without moving our eyes, but not clearly. Typically we can see movement to the side of us. When this happens we say: out of the corner of his/my/etc eye
It is also possible to say "out of the corner of his eyes" (plural) in a situation where you notice movement on BOTH sides of you, eg:
"Out of the corner of his eyes he could see people creeping up behind him." (on both sides)