You can only do a private party sale to another resident of Illinois. If your buyer is out of state, you will have to ship the rifle to an FFL holder in his state.
If your buyer is an Illinois resident, you must get his name, address, FOID, number, & expiration date and keep that information, along with a legal description of the firearm, for 10 years from the date of the sale. Also, you will be required to withhold delivery of the rifle for 24 hours after your buyer has agreed to purchase the rifle.