I found this by searching remove oil stain from leather and their were several more to look at.
Oil Stains From Food, Skin, And Hair
I received a panic call from a lady whose son had just that minute brought home a hot pizza and placed the box on her new sofa. The oil and cheese had leaked onto the leather. I gave her these instructions with the first step being to dump corn starch onto the stain. I called her back a week later and she said “Oh yeah, it worked great”. My guess is the powder absorbed the oil faster than the leather could. Of course I don’t know how large an area was affected. This is the best emergency action for sudden problems.
Small oil stains can be treated and successfully removed if you have the patience. Corn starch (or in a pinch, talcum powder) rubbed briskly into the stain with your fingers until the heat from the friction is felt. That heat loosens the oil and allows the corn starch to absorb the oil before the leather can. Vacuum or brush the powder off. Repeat until the stain is gone. This method rarely takes out any color but does take out the oil. Patience and persistence are the keys to success.
Larger stains from head and hand oil require time in our shop.
Good luck.