Google has yet to officially announce a date, but according to Canadian carrier Telus, it seems that they are pretty confident that the update will be released on the 5th of October. This is according to a listing on their website that pegs the 5th of October as the date that both the Nexus 5 and Nexus 6 will receive their Android 6.0 Marshmallow update.
However they have also noted that these dates are subject to change, so either Telus knows something we don’t, which wouldn’t be surprising given that they are a mobile carrier company, or they might be using the 5th of October as a placeholder date, although it does admittedly seem to be rather specific.
That being said, Google will be hosting an event on the 29th of September in which the new Nexus handsets are expected to be announced, so we wouldn’t be surprised if Google also took the opportunity to announce the release date of Android 6.0 then as well.