Anytime tires sit for any extended period, the oils will settle and eventually leach out or evaporate. Dirt/Grass does speed this process up a bit (so does sun, high temperatures, lack of movement).
We use old mudflaps under the tires to isolate from the concrete pad we park on, and it helps to minimize contact with a surface that can create issues. Over time, they will still age out.
Something as simple as 2x pressure treated material will help with the dirt. At that point, it's also how much settling will occur.