How to reply a faculty to ask him to recommend you to another faculty who might be recruiting this year? I am a graduate school applicant for PhD in XXX engineering, fall 2021. I contacted a POI for the same and got the following reply:

Hi hashbrown,
sorry at the moment, the only graduate student position I have available is for YYYY research.
Thanks

Can I ask them to recommend my name to another faculty in the same field?
No - this professor doesn't know who you are or if you're any good. They saw your research interests, and they didn't align to what they're looking for right now. Somewhat doubtful they even read your CV.
If they didn't say &quot;I recommend you contact Dr. Y,&quot; then there is nothing material you can get from them.