Illinois would allow hunting and trapping of bobcats under legislation headed to the governor.
The House approved a plan Sunday that would establish a hunting season for the previously endangered animal.
A spokeswoman for Rauner, an avid hunter, declined to say whether the Republican has a position on the matter.
Democratic Rep. Patrick Verschoore of Milan says there are 3,000 to 5,000 bobcats in the state.
He says the predator was taken off the endangered species list in 1999 and its growing numbers pose a nuisance and potential danger.
State-issued permits would allow no more than 300 bobcats to be taken during a season running from Nov. 1 to Feb. 15.
Environmental groups remain opposed to hunting the cats.