There are a number of people who are snoring with mouth closed and often they seek solutions but there are not so many good resources for them.
First of all, just to state the obvious in case some people have not realized this – if you snore while your mouth is closed then your snoring is nasal or originating from your nose. Therefore do not seek solutions which target the mouth or throat snoring cases as they will not work for you.
Remember snoring is a vibration of tissue which happens when the air is trying to pass through a passage and this means that something in your nasal passages is vibrating and resulting in your snore.
So what you can do is identify what the root cause is by having someone look in your nose. It could be just as simple as that. Otherwise you may have to go to an ENT clinic for them to check it for you.
Also remember to try some basic things like cleaning your nose before going to bed, trying to sleep in different positions (it could be that there is an issue in one nostril), and maybe even try inhaling steam with the aim of clearing up your nose.
Other things which may help you are snore solutions which target nasal snoring such as nasal dilators and nasal strips.