Is it possible to have a fungal disease in the brain?

Yes: A number of fungi can cause meningitis or brain abscesses. Coccidiodomycosis meningitis is not rare in the sw usa. There was a recent severe nation wide outbreak of fungal meningitis, all over the news, due to contaminated compounded corticosteroids. Mucormycosis can invade the brain from the nose.

Unusual, but yes: Fungal infections of the brain are unusual, but do occur. They are most commonly seen in people with compromised immune systems, or in those who have had the normal protective barriers of the brain bypassed. One recent example of the latter is the outbreak of fungal meningitis in patients getting epidural injections with contaminated medications.