Neville, who last served as an assistant to his brother Gary at Valencia, is apparently looking for a route back into football management. The FA is expected to speak with the 40-year-old as it kicks up its recruitment drive.
Neville also served as a coach on England's Under-21 side before joining David Moyes' staff at United.
"Management is something I do want to do, whether it's today, whether it's tomorrow, or whether it's in six months or six years," Neville said Thursday, according to Sky Sports. "It's something that I will have to do. I've had two great experiences as assistant managers at United and at Valencia, but now is the time where, for me, I want to be a manager and not a No. 2 or an assistant."
The FA dismissed Mark Sampson from the job in September after an internal investigation discovered evidence of "inappropriate and unacceptable behaviour" during his time in charge of Bristol Academy. His firing came amid separate allegations of bullying and racism towards former English international Eni Aluko.
It's unclear whether England will install a permanent manager before its next batch of competitive fixtures at the SheBelieves Cup in March.