A possible PhD invitation situation but no reply over time

Question

​​I once interviewed with a professor for a PhD position, but was rejected due to lack of local language skills. However, the professor mentioned that he will let me know when he has another position, because he really wants me to join them.

I thought it was a polite remark at first, but I received a PhD invitation from the professor just one month after the interview. He asked “Would you still be interested to join us? possibly I may have an option for another PhD. (not sure yet, but very likely). So I officially replied that I would like to join their team, and the professor also replied that he would reply within 5-6 days depending on the situation, but it has been more than a week since the reply time.

I was thinking how should I ask the professor about the situation?

In addition, I also wondered if I was overly serious about my reply and overly polite, causing him trouble?

Answer 1

Don't read anything into a delay of a few days. People are busy. People are forgetful.

If you have another option, then continue to follow up with it. If you are at a decision point, then ask again about the position and your likelihood of fitting it.

On the other hand, also be sure that you keep your own best interests at the forefront. There are a few (hopefully few) situations in which a new professor has a need for a student and that need overcomes good sense.