The Storm Prediction Center (SPC) has issued a mesoscale discussion (MD) for a large portion of Northern and Central Illinois, which you can read below.
In short, there is an 80% chance of an issuance for a Severe Thunderstorm Watch, so a watch is likely in the next hour or two. Damaging winds looks to be the main threat.
Mesoscale Discussion 0974 NWS Storm Prediction Center Norman OK 1223 PM CDT Sun Jul 01 2018 Areas affected...Northern and Central Illinois and Far Northwest Indiana. Concerning...Severe potential...Watch likely Valid 011723Z - 011900Z Probability of Watch Issuance...80 percent SUMMARY...Strong to severe storms are expected this afternoon across northern and central Illinois. The primary threat from these storms will be damaging wind gusts. DISCUSSION...Temperatures have risen into the mid to upper 80s across much of Illinois with dewpoints in the upper 70s. This has led to MLCAPE around 2500 J/kg. Additional destabilization is expected through the afternoon as surface heating continues. Storms are expected to form along the cold front (currently in eastern Iowa and Eastern Missouri) and move eastward through the afternoon. Flow is relatively weak on the ILX 12Z sounding, however, low-level flow is forecast to increase to 35 to 40 knots by mid-afternoon. This will lead to a marginal shear environment with effective shear around 25 to 30 knots with most of this shear focused in the lowest 1 to 2 km. Nearly parallel orientation of the cold front to the deeper level flow will limit a greater severe weather threat, however, more robust updrafts could mix down stronger winds, posing a damaging wind threat through the afternoon. The threat will be maximized with any bowing segments which can orient more normal to the low-level flow and accelerate northeastward. A severe thunderstorm watch is likely in the next hour or two to cover this severe wind threat.