Thanks for the question. First of all, Satan is a created being (Ezekiel 28:15), and he is certainly not God, though he would like to be (Isaiah 14:13-14). And, of course, this is what he promised Eve (Genesis 3:5). In Job 1:7 Satan said that he had been “roaming about on the earth,” which surely doesn’t sound like omnipresence. Also, in Job 1:6 Satan came before God. In Revelation 12:9 Satan is cast down to earth, out of heaven. Again, this would be impossible if Satan were omnipresent.
Satan has a network of demons, and these (like angels) seem to have a certain restricted territory in which to function (Daniel 10:20; 12:1). I take it that since Satan has demons strategically placed around the world, he is kept informed as to what is happening in the world, but this is not omniscience, nor omnipresence.