It's not about seeming desperate or not, that's something you shouldn't even worry about. The thing is, staying in doubt eats at you way more than a direct conversation, even if it goes badly. That said, before you call maybe try something first: send him a message different from usual, like a question about something you know he's interested in or an inside joke you two always do. It's not to "test" him, it's genuinely to figure out if the problem is he's gotten tired of the current dynamic or if he's actually going through a rough time. Sometimes people stop responding when the conversation becomes too "light" or routine, not because they're dropping you.
If even that doesn't budge anything, then you should really communicate. A call though is a lot, maybe keep that as plan C. Try first with a more direct message like "hey, feels like we haven't been in touch much lately, you good?" without cornering him but giving him space to open up. If he keeps ghosting even that, well, then you've got the answer you were looking for and at least you didn't drive yourself crazy wondering about it for months.