Firstly, let me list the two words involved:
- In Rom 3:11, "seek" translates the verb ἐκζητέω (ekzeteo) = seek out, search for, required, etc, eg, Luke 11:50, 51, Acts 15:17, Rom 3:11, Heb 11:6, 12:17, 1 Peter 1:10. [I note that Heb 11:6 uses the same verb to describe people who seek God.]
- In Acts 17:27, "seek" translates the verb ζητέω (zeteo) = seek, search, eg, in Matt 2:13, 20, 6:33, 7:7, 8, etc. [I note that these first few all describe people seeking God or Jesus.]
Thus, Rom 3:11, which says that no one seeks God, appears to quote Ps 14:1-3 and Ps 53:1-3.
The previous verses clarify the "problem" here because we read that:
Rom 3:9 - What then? Are we any better? Not at all. For we have
already made the charge that Jews and Greeks alike are all under sin.
Thus, humans, as they are born and in their natural, unregenerate state (Ps 51:3, 5) do not seek after God. However, (and this is the imports caveat) the Holy Spirit prompts such sinners to seek God, even before conversion.
- 2 Cor 5:14 - For Christ’s love compels us ...
- Phil 2:13 - For it is God who works in you to will and to act on behalf of His good purpose.
- John 6:44 - “No one can come to Me unless the Father who sent Me draws him, and I will raise him up at the last day.
- Rom 2:4 - Or do you disregard the riches of His kindness, tolerance, and patience, not realizing that God’s kindness leads you to repentance?
- Rom 5:5 - And hope does not disappoint us, because God has poured out His love into our hearts through the Holy Spirit, whom He has given us.
- Eph 2:5 - made us alive with Christ even when we were dead in our trespasses. It is by grace you have been saved!
- John 16:8 - And when He [the Advocate, Comforter, Helper = Holy Spirit] comes, He will convict the world in regard to sin and righteousness and judgment
Thus, it is only by God via the Holy Spirit that anyone seeks God. Put another way, Salvation is the initiative of God and the only ones who seek God are those who respond to the prompting or "drawing" of the God.