(Rom 2:7 ESV) to those who by patience in well-doing seek for glory and honor and immortality, he will give eternal life;
(1Co 15:54 ESV) When the perishable puts on the imperishable, and the mortal puts on immortality, then shall come to pass the saying that is written: “Death is swallowed up in victory.”
In fact, to receive eternal life is to receive the gift of immortality. The damned, therefore, remain mortal.
God alone is by nature immortal —
(Rom 1:23 ESV) and exchanged the glory of the immortal God for images resembling mortal man and birds and animals and creeping things.
(1Ti 6:15-16 ESV) 15 which he will display at the proper time — he who is the blessed and only Sovereign, the King of kings and Lord of lords, 16 who alone has immortality, who dwells in unapproachable light, whom no one has ever seen or can see. To him be honor and eternal dominion. Amen.
So we are born mortal, subject to permanent death, but God can give us eternal life, that is, immortality.