Is it normal ? I wasn't here when the old halving block rewards happened before so I'm not sure how things work exactly but logically ... should we see a price increase (at least little bit) since we are getting closer and closer ?
There is no "normal".
One halving has occurred so far.
The price reacted long after.
Was it because of the halving?
Was it because of the sustained attention that Bitcoin was getting due to Ross Ulbrichts arrest?
Or was it because of shenanigans at Mark Karpeles's exchange, a bot running rampant, trading coins that didn't actually exist?
So, no there's no reason to think that it's a given that the price should increase, just wishful thinking on everyone's behalf.