Truthfully, there is no such thing. And here is why. The will involves the choices we make. It always does what it most desires, and indeed it is free to do so. Something must be in our mind that moves our will, our choices one way or the other.
For example, one may desire to skydive out of a plane for the experience of doing so would give them. At the same time they know they are afraid of heights, know there will be a point before jumping of fear of the possibility of failure of gear, or being frozen by fear, the potential of great harm or death being the end result of jumping out of that plane. And this is much stronger that any imagined pleasure in skydiving, and our will, or choice is "No. Not ever!"
And here we run smack into the no freedom of the will. Our will is free to move us in the direction of our desires, it can do what we desire, but it cannot do what we do not desire.
If we move this into the place free will is usually moved in order to state that God gave us free will, therefore it is up to us to choose Christ, if our doctrine leading up to this place is sound according to the scriptures, that God is holy, and we are sinners alienated from Him, we will find a very interesting conclusion. If we insist on free will to choose Christ in spite of all the evidence concerning the will that has been pointed out, we will simply ignore it and keep repeating our free will belief in spite of the logical evidence given in the scriptures. We will care more about our comfort in our belief, for whatever reason, than whether it is true or not. We will continue to trust in our supposed free will choice for Christ, rather than trust God who says if you believe in the person and work of Christ, I have saved you.
In our natural fallen state, we do not desire God. The Bible tells us we are at enmity with Him. We have sinful desires and we take pleasure in them. We also have desires that are not sinful, but it remains that we sin because we are sinners. The unregenerate man does not see his sins as sin against God. The unregenerate man does not even like the word sin, and often scoffs at and mocks it. It is an old fashioned word to them, that is the product of "Jesus freaks." And to them it is one part of society trying to control all parts of society, restraining their fun.
Let's look at through an example the different reaction to a sin between the unregenerate and regenerate. Those in Christ know the Bible says to be drunk is a sin, mainly I think because many a sin is committed while being drunk. The Bible does not condemn the consumption of alcohol completely but only getting drunk. Which, let's face it is usually the reason for drinking. A Christian may fall victim to this desire, but his remorse the next morning is directed towards the sin he has committed towards God in displeasing Him. And he determines to never do it again, which may come to pass, or may not. Depending on which desire is greater in any particular moment, and his stage in the process of sanctification.
The unregenerate may make the same vow but for an entirely different reason. One that has nothing to do with sin or God, as he does not even consider it a sin. His reason is based solely on the way he feels the next morning if he has a hangover, or the embarrassment or shame he feels if he has made a fool of himself, or hurt someone, or wrecked his car etc. And even if the impact of the night before is so great that he never drinks another drop, he goes on sinning in other ways that he does not recognize as sin and quite likes.
So the unregenerate person cannot choose Christ because he has no desire to, does not know Him, and feels no need of Him. It is like my brother once said before he was placed in Christ and people preached the gospel to him. "Who is this Jesus you talk about and say loves me? I thought He died."
The unregenerate has a will that is free to choose what it desires, but one that is not free to choose what it does not desire. Just as is the case with every choice made.
The one who has been regenerated, something only God can do, has his desires changed by the grace of God. Those desires having been deeply seated in us through Adam, holding us captive to sin. These changed desires are described in scripture as being given a new heart. Not us changing our hearts and desires, but God giving us a new heart, placing us in Christ. Our desire now is for Him (a choice by necessity).