It’s been talked about for years, both among some Memphians, and among roadgeeks. However, it looks like the idea of a third bridge across the Mississippi River at Memphis might be getting additional attention, judging by this article in the Arkansas Democrat Gazette:
Increased traffic counts over the two Mississippi River bridges in West Memphis and the resulting longer delays for motorists traversing the two spans have local officials studying the possibility of constructing a third interstate bridge.[...]
But it may be the first time that the necessary parties are all on the same page, said Eddie Brawley, director of the West Memphis Planning Organization. [...]
Tentative plans call for installing a bridge at the southern edge of West Memphis, through the city’s industrial park and the river port. The bridge would cross the Mississippi River there and reconnect with Interstate 55 south of President’s Island near downtown Memphis.
Another idea is to build a bridge just north of Marion. The bridge would merge with the northern loop of Interstate 40 in northwest Memphis.
Considering traffic flow in the region, the location of the Ports of Memphis and West Memphis and the assorted truck depots, I’d think the West Memphis - President’s Island alignment. After all, it’s closer to where much of the long-haul trucking in the area is destined for, and it probably provides the greatest relief from the bottleneck on the east end of the I-55 bridge—the cloverleaf interchange connecting I-55 through southwestern Memphis with the bridge itself.