Why was I advised to contact prospective advisors when following up on my PhD application? I applied for a PhD program in a US university for Spring 2021 in the 1st week of August, 2020. I have mentioned a professor's name and work, who encouraged me to apply and permitted me to write his name in the SOP. However, after 1 month, in the reply to my follow-up email, the graduate coordinator advised me to contact prospective advisors in the department.
Two possible things in my mind:

The grad coordinator has not read my application or has not noticed my possible adviser's name in the SOP.

The grad coordinator has sent the application to the professor and the professor declined to take me in his lab. Thus, the grad coordinator advised me to find other advisers for funding.


What might be the reason?
My best guess is that it was just a standard reply. Otherwise I think you would have gotten more information.
But you should contact that professor again and discuss the state of your application and whether they are still willing to take you on.
Don't make assumptions here.