God’s omnipresence is one of His essential attributes. His justice is also essential, and, therefore, it is necessary for Him to punish sinners who do not trust in Jesus for salvation. Thus, we have a God who is referred to as everywhere present yet who maintains a place called hell, described as a place where people are removed from His presence (see Matthew 25:41).
Three passages are particularly important to this discussion. First is Psalm 139:7–12, in which David says, "Where shall I flee from your presence? If I ascend to heaven, you are there! If I make my bed in Sheol, you are there!" Sheol is simply a transliteration of a Hebrew noun that means “the grave” or “the place of the dead.” Sheol is a broad term and is not synonymous with hell, the word commonly used to refer to the eternal place of punishment.
Second Thessalonians 1:7–9 says that those who do not know God “will suffer the punishment of eternal destruction, away from the presence of the Lord and from the glory of his might” (emphasis added). Yet Revelation 14:10 says that any who worship the antichrist "will be tormented with fire and sulfur in the presence of the holy angels and in the presence of the Lamb" (emphasis added). These two verses are by far the most confusing on this topic because of their apparent contradiction. Even so, there is a rather simple explanation found in the original Greek.
In Revelation 14:10, "presence" is a literal translation of the Greek enopion, which means "in the presence of, before." This is a spatial word, suggesting proximity and literal, measurable distances. In contrast, the word translated "presence" in 2 Thessalonians is prosopon, which most commonly refers to a person’s face or outward appearance. Paul appears to have taken this verbiage directly from Isaiah 2:10 as found in the Septuagint. There are other references to God and His people being "separated," even on earth. Jesus’ cry of agony on the cross is one example (Matthew 27:46; Mark 15:34). Theologian Dr. Louis Berkhof teaches that Paul refers to "a total absence of the favor of God." This description of hell would present a more exact opposite to heaven. Heaven provides blessing and wholeness not through being closer spatially to God, but by being in complete fellowship with Him. Hell is associated with a complete lack of blessing due to the severing of any fellowship with God.
Ultimately, it appears that God is indeed "present" in hell, or hell is in His presence, depending on how one looks at it. God is and will forever be omnipresent. He will forever know what is happening in hell. However, this fact does not mean that the souls imprisoned there will have a relationship with God or any communication with Him.