The fact is that according to Scripture, God alone has immortality as a present possession:
Now to the King, eternal, immortal, invisible, the only God (1Tim. 1:17);
Who alone is immortal, and lives in unapproachable light. (1Tim. 6:16);
They exchanged the glory of the immortal God for images made to look like mortal man … (Rom. 1:23).
Immortality is a prize we are to seek after. Jesus tells us it will be granted only to those who are considered worthy (Luke 20:34-36). Paul says, To those who seek glory, honour and immortality he [God] will give eternal life(Rom. 2:6-9). In this latter case, we might ask, who seeks what one already has?
Eternal life in immortality is a gift given to the believer alone, and that gift is given only when Jesus returns (1Cor. 15:42-54).