I had a successful interview at this very small-sized market research company ( they have less than 7 people) about a month ago, and they recently informed me that my starting date is going to be late January next year.

I am happy that they are willing to hire me, but I am a little worried about how they are processing my application; they said they are quite busy and not sure how this role is going to look like. So they have not offered me the contract yet. Although I understand that this is the nature of the small firms, I would like to have some sort of assurance on getting this job from them so I can make sure that I start working from late January next year.

How should I go about approaching my employers about this?