The Bible does not say that Satan is able to read the minds of humans. And evidence from the Bible makes it appear that Satan does not have the ability to read our thoughts.
None of the descriptive names given to Satan imply that Satan has the ability to read minds: Satan (Resister), Devil (Slanderer), Serpent (synonymous with Deceiver), Tempter, and Liar. (Job 1:6; Matthew 4:3; John 8:44; 2 Corinthians 11:3; Revelation 12:9)
In fact, the apostle Paul assures us that Christians “are not ignorant of [Satan’s] designs.” (2 Corinthians 2:11) So we don't need to be afraid that Satan has some extraordinary ability of which we are entirely unaware.
However, this doesn't mean that he can't discern our weaknesses and vulnerabilities. Satan has been able to study human behavior for thousands of years and so he doesn't need to be able to read minds to discern what patterns of behavior we set. Even many perceptive humans can successfully surmise what other people are thinking or feeling by observing clues such as what entertainment they pursue, or to listen to what things they talk about, and so forth. Even our facial expressions and posture can give away what we may be thinking.
While Christians do not need to fear that Satan will read their minds, they do have reason to be concerned about what thoughts Satan might try to put into their minds. 1 Timothy 6:5 says that Satan wants Christians to become “corrupted in mind and despoiled of the truth.” Ephesians 6:17 tells us that we must protect our minds by wearing “the helmet of salvation.” We can accomplish this by filling our minds with Bible truths and avoiding unnecessary contact with corrupting elements of Satan’s system.
Satan is a formidable enemy. But the Bible assures us that we don't have to have a morbid fear of him. James 4:7 says: “Oppose the Devil, and he will flee from you.” Jesus successfully set this example and if we follow this counsel and example, Satan will have no hold on us. (John 14:30)