Does God desire the reprobates to become the elect? Here are resources to help answer that question.
Paul Manata made some good points in a comment section :
“If God doesn’t desire that any should perish, why doesn’t he save them all? He can’t obtain what he desires? Also, since I believe the Bible does teach that some people will be in hell forever, it is irrational for me to hope that all people will be in heaven forever. it’s like getting a news report from a very trustworthy source that a dirty bomb went off in the middle of Times Square, definitely killing some people. It would be irrational for me to hope that everyone made it out alive if I also believed the news report. I might hope that my friends who were visiting NYC at the time made it out alive, but not that everyone indiscriminately made it out alive. …
Yeah, I just don’t see God having that desire. If he knows that some sinner, S, will be in hell (indeed, God decreed it), then it makes no sense to desire the impossible—the salvation of S. It is irrational to desire what you know is impossible to have. if God truly did desire S to be saved, he would simply fulfill this desire. If S desires Ω, then S typically acts in ways to bring about Ω. God in no way acts to bring about salvation for S, thus it’s hard to see in what sense he could desire it, at least on action-based accounts.”
“It is logically impossible for those that Jesus did not die for to be saved
God does not desire that which is logically impossible
God does not desire for those that Jesus did not die for to be saved. I know 1 from Scripture. I know 2 because God is logical. I know three follows from two because the form of the argument is valid.”