I'm interested, I'm just drawing a blank about how to accomplish it. The problem with Libya being the basis for such a state is that the Sahara is in the way.
Ghaddafi is building a large rail system in Libya that is supposed to link Tripoli with Sabha, in the Fezzan. Maybe if that line were built first, it could be extended down into the Sahel, linking the region.
The other problem is that it can't be done militarily, since France will intervene.
The big problem is that the Sudan and Chad are weird countries that are half Christian and half Muslim. These two states would have to fragment for any of this to work.
So we'd need a TL where the 1st Sudanese Civil War results in Sudan splitting into a Christian South and a Muslim North - perhaps that give impetus to a splintering of Chad - that leaves two really, really, poor countries, which then enter a union with Libya which has lots of oil money.
Population, @40 million
GDP $170B PPP - 54th largest, between Kazakhstan and Finland. A dirt-poor place, and Libyans are going to have to bear a pretty huge burden, as they are half the economy and 15% of the population.