A degree of preference is perfectly natural. Just keep reassuring your partner of that. Most children go through a phase of preferring one parent over the other.
It happened in my family as well, with me as a baby, and then with my son - Your son is very young at the moment, but what was important for us was:
1 - make sure that both parents are doing sleep related care (putting to bed and more importantly, being there when they wake up). We found a huge preference formed if it was just me always being there every time he slept or woke up. Sleep is a very vulnerable time, and young kids can really latch on to the person that is with them through that.
2 - Force yourself to let them have 1-1 time, especially outside of the house. It just isn't the same if you are there - if it is always the baby + you, or all three, then of course the baby will bond far stronger with you. Let your partner take him out, alone, for afternoons/mornings.. give them plenty of time to bond - at that age, children bond far stronger 1-1 than in groups - although he might cry, you need to be strong and not jump back in. Going out is good because it is distracting and may reduce crying.
3 - He is too young for this, but as your child becomes old enough to have "interests" make sure that some of those are things that he shares and does only with your partner. So they become "Daddy" activities, that he associates just with daddy. That will help his understanding that both parents provide different things, and both are valuable. If you can give him all the play he needs, why does he need Daddy? But if only daddy plays football, or wrestles, or wants to talk about space ships, then Daddy has a purpose in his mind.