Till now there are no official dates available for the counselling. So its can't be concluded when it will start, but its expected to start in this month. Now to stay updated, I would recommend you to keep an eye on the career360.com (//career360.com) as it will give you the updates as soon as any notification comes out in NTA website.

To know more about the counselling and stay updated follow the link below:

https://medicine.careers360.com/articles/neet

I hope this answer helps. All the very best for your future endeavors!