I have worked in Y for 2 years as a research assistant and then I moved to my home country and worked here for almost 4 years and published papers in reputed journals. Logically I think I should include the names of my current supervisors or the supervisors I have published works with.
But Professor X (I am applying for a Ph.D. position) is originally from Y, currently residing in Canada. He asked me to include three references from Y. So I wrote the supervisors I have worked under.
So basically I wrote three of my supervisors two days ago and asked for their permission if I can include their name in my application and none of them replied yet. Maybe things are difficult due to this pandemic.
In this situation what should I do? Should I write Professor X that I could not reach them? Or just send Professor X the list of names? what if Professor X contacts them and they don't reply?
(I am restless because Professor X is waiting for my reply too)
People get loads of emails and it is very natural that some take a few days to reply. Also some emails may be missed or overlooked, so you can write again and say it's urgent. Normally such things should be done with a few weeks time if at all possible because answering to such requests is not the first thing on people's list.
If all else fails, try to contact somebody else. I'd avoid to give Professor X the list of names without having an answer from them. It doesn't look good to pass on such information without being authorised. You can ask Professor X for advice what to do without telling them names. Surely if Professor X is responsible for the tight time frame, they should have some understanding.