Most Protestants say no. Many Catholic authorities also say no or that they are unsure. Reflecting upon this question, my response would be that it depends. What do I mean?
First, Protestants say no because there is little or no Scriptural evidence that Satan has this ability. Of course, the Bible is about God and his promises to his people that are ultimately fulfilled in Jesus Christ. It cannot be used as a text upon demonology.
Second, Catholics and others would emphasize that the devil as a creature is not omniscient and everywhere like the Lord. He has certain angelic powers, which are not entirely clear, but like us he is limited. As an angel, albeit fallen, he exists as a spiritual being outside of time and space. However, if he wants to interact with physical creatures then it would seem his focus would be limited to one place at a time. Of course we also refer to the devil in terms of his many minions among the demons that accompanied him in their fall from heaven. They can afflict us even if their master is not immediately present. Similarly, St. Michael the Archangel employs (on behalf of the Lord) a host of guardian angels to watch over us.
Third, even if Satan or any other fallen angel cannot read a particular mind, they can still anticipate what we might be thinking and subsequent human behavior. Human intellect pales in comparison to the angelic and they can easily deduce what we might be thinking through minimal external details.
Fourth, we as Catholics believe that God somehow makes it possible for us to bring our mental prayers to the saints that they might pray for and with us. It may be that what God facilitates in heavenly communication, he permits in the misuse of human freedom toward the demonic.
Fifth, given this reality in prayer, I suspect that we would not have to verbally or audibly address spiritual evil so as to be heard. Thus, while devils cannot generally read minds, such may become the case if a person directs or mentally projects his or her thoughts to the demonic. The demons have no physical mouths and so they must communicate in such a fashion with one another. Because of the veil between this world and the next, we can transmit but we are not as good at receiving communication from the other side. Indeed, other than prayer, we are forbidden to instigate communication with the dead and/or the demonic. There is a great danger in any possible response. Any favors or supernatural abilities given come with a dire price. It opens the person to possible diabolical manipulation as through obsession or even possession. It can cost us our souls.
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