This is not true. We were *dead* in our trespasses and sins (Ephesians 2:1 and 5). Dead people do not desire anything. It is instead *by grace* that you are saved, as a response to One seeking you.
Here's Ephesians 2:1-9:
And you he made alive, when you were dead through the trespasses and sins in which you once walked, following the course of this world, following the prince of the power of the air, the spirit that is now at work in the sons of disobedience. Among these we all once lived in the passions of our flesh, following the desires of body and mind, and so we were by nature children of wrath, like the rest of mankind. But God, who is rich in mercy, out of the great love with which he loved us, even when we were dead through our trespasses, made us alive together with Christ (by grace you have been saved), and raised us up with him, and made us sit with him in the heavenly places in Christ Jesus, that in the coming ages he might show the immeasurable riches of his grace in kindness toward us in Christ Jesus. For by grace you have been saved through faith; and this is not your own doing, it is the gift of God-- not because of works, lest any man should boast.
Thanks Theo, you are absolutely right, great verse too.