Scripture defines the term "inner man" as being the spirit of a man. And further, it teaches that an alive and active and growing inner man is a man's born again spirit possessed only by an individual who is born again believer:

[Compare 2 Cor 4:16]:

"Therefore we [believers, v. 5] do not lose heart, but though our outer man [the sin nature] is decaying, yet our inner man [the born again spirit] is being renewed day by day."

[Compare Eph 3:16]:

"That He would grant you, according to the riches of His glory, to be strengthened with power through His Spirit in the inner man..."

[Compare Ro 7:14-25]:

(v. 22 cont.) "For I joyfully concur with the Law of God in the inner man..."

(v. 23) but I see a different law in the members of my body, waging war against the law of my mind, and making me a prisoner of the law of sin which is in my members.

[The law of my mind ? the law of God which pervades Paul's born again spirit = his inner man, (cp. v. 25)]

(v. 24) "Wretched man that I am! Who will set me free from the body of this death?"

[Although Paul is indicated here as a born again believer with an "inner man" he, like all believers who are still physically alive, possesses a mortal body which deteriorates daily. And pervading throughout the members of that body is the ever present, adversarial sin nature which obeys the law of sin and opposes the law of God which is within Paul's "inner man" - his born again spirit. But Jesus Christ, Whom Paul has trusted in for eternal life, will eventually set Paul and all believers free from the wretchedness of their sin-contaminated, decaying fleshly bodies - providing them with new, immortal, perfect ones with righteous natures, (I Cor 15:50-54)]:

(v. 24 cont.) "Wretched man that I am! Who will set me free from the body of this death?

["Who will set me free from the body of this death." ? Who will provide or how will I be "set free" from this body of mortal death so contaminated with the sin nature? And the answer comes in the next verse]:

(v. 25) Thanks be to God through Jesus Christ our Lord! So then, on the one hand I myself with my mind am serving the law of God, but on the other, with my flesh the law of sin."

Notice again, that whenever this took place in Paul's life, we see that Paul had two warring natures: a sin nature and a born again, Holy Spirit indwelled "inner man" - an alive spirit which must be alive because it is serving the law of God. No unsaved individual can serve the law of God, (Ro 8:8). Compare Ro 8:10 which verifies that a believer still has a sin nature:

[Ro 8:10]:

"And if Christ is in you, though the body is dead because of sin, [sin singular ? sin nature] yet the spirit is alive because of righteousness."

Although the body of the believer is dead because of sin, i.e., destined to physically die yet the believer's spirit is alive:

"Yet the spirit is alive because of righteousness" ? Yet the spirit is alive because it is born again - because through faith alone in Christ alone one has had their spirit become alive, i.e., born again and has received the righteousness of Jesus Christ,

(ref. Ro 3:21-24).