private speech
My answer would be no, shaitan cannot read our minds. From my knowledge, shaitan is basically jinn and humans who tries to influence our actions. Can jinn or humans listen to our private speech? My answer is no. Even angels don't hear our private thought. They can only witness what we do physically and say out loud. i.e angels witness the recitation of Qur'an during dawn, and by recitation it means in a soft voice, not too loud nor in our mind (private speech).
Only Allah hears everything.
Allah knows best.