To chase or not to chase?

I met this guy at work and we exchanged Instagram names (not numbers). My coworker said he was a really shy guy even though he's attractive and just doesn't talk to girls, so keeping this in mind I messaged him first. We had an awesome conversation that lasted all day to 2am. And he said he wanted to see me again and asked me what I wanna do for my bday... but he still didn't ask for my number. I thought he should initiate next time we talked but we haven't talked at all since then and I don't know if I should message him first again or what. so should I just give up on him or keep initiating... like forever...
To chase or not to chase?
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