I am in the process of contacting a potential supervisor to pursue a PhD in his group. We have agreed on the project and that I am a good fit for the project. However, there remains the funding issue. The professor is only granted funding for a UK citizen (since it's a university in the UK) from the department. But since I am an overseas student (the fees are double that of UK/EU citizens) he has to make a case to convince the department to fund me. I emailed him once, a week after our agreement, asking about updates regarding this situation. I got an update but no definitive yes-no answer and I am still waiting for more information. He said he would contact me when he has more information. But it's been more than 10 days since our last contact and I haven't received anything. Should I email him again? If so, what should I mention in the email (without seeming too pushy)?
I wouldn't push unless I had another option to consider and might need to back out of acceptance for another position. Ten days isn't a lot of time to move a bureaucracy.
However, if you need to write to him on another legitimate matter you could add a note at the end whether anything has developed about funding. If your acceptance is contingent on funding he should know that.