Let's fill in the blanks with the correct form of the verbs. In this case, we need to use the verb 'hear' and 'come in'.
The most appropriate structure here is to describe hearing an action in progress. We can use the structure 'hear someone doing something'. Thus, the verb 'come in' should be in the '-ing' form.
So, the answer is:
I heard him coming in.
Translation: Я слышал, как он входит.