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First time I have read of a plan to invade Illinois. Bragg invaded Kentucky in June of 1862. The campaign ended in failure. Had Bragg been successful in Kentucky, then Southern Ohio and Southern Indiana might have been considered for further operations. With the Union holding a big portion of West and North Tennessee, Illinois would appear to be out of the question. JMO

Found a reference to it, though not exactly what I wanted:

"Davis offered his advice to Albert Sidney

on repairing the Confederate situation in the West.
His ideas were aggressive and optimistic despite the fact that he knew that the South's forces there were outnumbered and inadequately armed, the Confederates being forced to rely upon private weapons to make up the shortfall.
'With sufficient force," Davis wrote, 'the audacity which the enemy exhibits would no doubt give you the opportunity to cut some of his lines of communication, to break up his plan of campaign, and, defeating some of his columns, to drive him from the soil as well of Tennessee as of Kentucky.'
Davis believed the Union would aim at the Tennessee and Mississippi rivers in its next campaign and hoped Johnston could concentrate enough force to counter such a campaign.
Additionally, Davis hoped a move by forces under Edmund Kirby Smith into eastern Tennessee would create a diversion.

**So here it comes**

A Confederate fleet was also gathering on the Mississippi River.
If the Union moved its gunboats up the Tennessee, it would give Johnston a chance to strike at Cairo, Illinois.
Davis correctly deduced the Union river campaigns, which were in some respects dictated by geography and logistics, but he was overly optimistic, indeed unrealistic, about the potential for a Confederate naval strike against Cairo."
Stoker, "Strategy and the US Civil War" (2010), p 116

So, it was not an invasion of Illinois Davis planned, so much as a naval raid on Cairo, which could mean Davis' plans were foiled less by Grant at Fort Donelson than by Union General John Pope's canal dig and assault on Mississippi Island No. 10 (Kentucky Bend) in April 1862.