Proverbs 2 calls the reader to seek wisdom avidly, with the promised result that we would understand the fear of the Lord and the knowledge of God. This struck a chord, in that the prayer in Colossians 1 seeks a movement from knowing God’s will (similar to wisdom) and results in “increasing in the knowledge of God.”
Knowledge is a broad concept in English, but we can distinguish between knowing about someone (i.e. his will, his attributes, his history) and knowing someone personally. Spanish uses saber for knowing things and conocer for knowing people.
Compare these two texts for yourself.
Proverbs 2:1-5 – ESV
My son, if you receive my words
and treasure up my commandments with you,
 making your ear attentive to wisdom
and inclining your heart to understanding;
 yes, if you call out for insight
and raise your voice for understanding,
 if you seek it like silver
and search for it as for hidden treasures,
 then you will understand the fear of the Lord
and find the knowledge of God.
Col. 1:9-11 – ESV
And so, from the day we heard, we have not ceased to pray for you, asking that you may be filled with the knowledge of his will in all spiritual wisdom and understanding,  so as to walk in a manner worthy of the Lord, fully pleasing to him, bearing fruit in every good work and increasing in the knowledge of God.  May you be strengthened with all power, according to his glorious might, for all endurance and patience with joy…