No, he cannot. There are no scriptures which teach Satan can read our minds. But Satan and his demons can observe us. Many times it's no small jump to recognize what a person is thinking. For instance, if a child is starring at a toy in the store, we can guess that he probably wants it. When he verbalizes his desire and reaches for the toy, then his thoughts become known. Similarly, our words and actions serve as an index to our minds. Our past behaviors also reveal where our fallen natures have sinful tendencies. Yet, in this same manner, we can know Satan's thoughts!
Consider 2 Cor. 2:11, "Lest Satan should get an advantage of us: for we are not ignorant of his DEVICES "(Greek "noema", Strong's G3539) "Noema" means purpose, intellect, or mind. The scripture proves we are not ignorant of Satan's thoughts either. We know he is the father of lies, that he tries to represent himself as an angel of light, that he hates and wants to destroy Christians.
In the story of Job, Satan attempted to destroy Job through the destruction of his things, the death of his family, physical diseases, and wrong arguments from his comforter friends and his wife. Satan used his whole arsenal to attack Job. If the Devil had had the power to read and enter Job's mind, he would doubtless have used it.
From our own experiences, I think we can attest wrong thoughts may enter our minds without warning. The ideas seemingly come from nowhere. It may be that Satan might be able to suggest evil thoughts. But regardless of the thoughts' origins, we do have scriptural counsel as to how to combat these evils. "Resist the devil, and he shall flee from you." (James 4:7) "Put on the whole armor of God, that ye may be able to withstand in the evil day,…and above all, taking the shield of faith, wherewith ye shall be able to quench all the fiery darts of the wicked…and the sword of the Spirit, which is the word of God" (Eph. 6:13, 16, 17) Reading, memorizing, believing God's word gives us great protective power. And finally, that which we cannot do in our own strength, God will do for us. "And my God will supply every need of yours…and the peace of God, which passeth all understanding, shall keep your hearts and MINDS through Christ Jesus." (Phi.4:19, 7)
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