No, nothing actually proving any correlation. I recall reading one study suggesting there is a coloration and then reading another study showing an inverse coloration (mild hearing loss being correlated to louder tinnitus). Neither study was very conclusive and both had very small sample sizes from what I recall. Suffice to say I don't think there is any correlation between tinnitus loudness and the severity of hearing loss.
There is a correlation between tinnitus and hearing loss, in that most people with tinnitus will show some amount of hearing loss even if it is "hidden hearing loss" and is undetectable on a standard audiogram, but the severity of tinnitus does not seem to be related to the severity of hearing loss.
That being said, it's much harder to mask or distract from the sound if you have severe hearing loss.