Neville, who has a Uefa Pro Licence and lives in Valencia, was an assistant to England Under-21 boss Stuart Pearce in their disappointing 2013 European Championship campaign.
He joined David Moyes at Old Trafford, where he lasted the 2013-14 season, despite the Scot being sacked.
His next top-level coaching job was at Valencia, where he was appointed coach in July 2015 and left soon after brother Gary was dismissed as manager following a run of three wins in 16 league games.
His experience and knowledge of the women’s game is understood to be limited, and opinion is mixed about whether he is the right person for the job.
England and Chelsea midfielder Katie Chapman said: “Surely there must be coaches out there who’ve had a lot more experience in the women’s game, and of actually being a manager?”
But former England goalkeeper Rachel Brown-Finnis said: “I think he is a great fit for England and he would inspire me.
“This is someone who has worked under Sir Alex Ferguson and is from a group of players who have lived with a winning mentality their whole careers.
“That is something which this team has never had, and needs to take it to the next level: a leader who knows what that looks like.”