The FAW have approached Chester City about speaking to Rush and have been given permission to talk to the former Liverpool great by Vaughan.
Vaughan said: "The FA of Wales have approached us and we will not stand in his way. Whether he will take the job, or do it full-time or part-time and stay here I can't say yet. We would love him to stay here but we won't stand in his way.
"He has done a magnificent job for Chester and is going to be a top manager one day. It's a big opportunity for him."
Chester City are now within one point of the play-offs after being adrift at the bottom of League Two when Rush took over.