How to ask a professor to introduce other professors to me when he mentions that he has no funding?
Don't ask the professor for contacts to other professors where you could apply - there's a risk that he will perceive it as annoying, and in principle it is work that you could easily do on your own.

Instead, you could add something like the following to your response:


  Please feel free to forward my documents to any colleagues who could be interested in working with me.


This will put the professor more in a mindset of helping some colleagues to find a (hopefully) good student, which he might be more willing to consider instead of helping a random applicant to find another job opportunity.