Historically, I have a horrendous fungus problem in my garden. When my tomatoes and other plants start showing tell-tale signs (spots on leaves, sick plant in later stages), my basil starts getting that same coloration.

It happened this year too. I did the same as I did for the rest of my garden and it cleared right up. I removed the discolored leaves treating them like toxic waste- total removal and hand washing after. Then I spray immediately with an organic copper based anti-fungal.

My basil really perked right up after I did this. I'm no expert.. but would suspect fungus. Maybe it's nothing, hopefully others will chime in.

My area is super hot and dry and I still have the fungus problem but it seems to set in during rainy/muggy weeks.

I've been spraying every Saturday morning and the discoloration has not returned.

Good luck!