The former Manchester United, Everton and England full-back has had talks with Martin Glenn, the Chief Executive and Baroness Sue Campbell, the head of women's football, this week - after the FA's Technical Director Dan Ashworth made contact in December.
Neville has no previous experience in the women's game and in spite of the fact that he has held an FA UEFA pro-licence qualification since 2013, it will be the 40-year-old's first spell in management.
Since retiring as a player, Neville took a full-time coaching role under David Moyes during the Scot's tenure at Manchester United in 2013 and also became a coach at Valencia in 2015.
Speaking on BBC Radio 5 Live, Chelsea defender Claire Rafferty was one of the first to suggest that Neville was in consideration for the role by saying: "Phil Neville's in the running for it.". However, the left-back later added she didn't know the scale of this interest.
Who else is in the running for the England job?
The FA have delayed the appointment of the new full-time England manager as they are committed to 'getting the right person' according to FA Chief Glenn.
With the original plan, which Baroness Campbell laid out in October of last year, was for the manager to be in place by the end of 2017 and in charge for the Lionesses trip to La Manga this month. Many of the obvious candidates for the role, however, have been discounted by the FA or taken up various roles elsewhere in the footballing sphere.
Mo Marley has been the interim manager of the England team since the departure of Mark Sampson and it is understood that the England under-19 coach, who is popular amongst the players, fans and staff, put her name forward to take on the role on a more permanent basis.
Former England defender Marley has been in charge since September and has led the team to 4-0 and 5-0 World Cup Qualifying wins over Bosnia and Herzegovina and Kazakhstan respectively.
John Herdman
Herdman was heavily linked with the vacant England job following an assertion he made back in 2013 when the County Durham native said he would consider the role following Sampson's appointment.
The 42-year-old, who took charge of the Canadian women's team in 2011 and led them to a World Cup quarter-final and two Olympic bronze medals, ultimately chose a different vacancy in football.
The Englishman has recently been named head coach of Canada's National men's team, who are ranked 94th in the FIFA world rankings and did not qualify for the final six-team CONCACAF qualifying group for the 2018 World Cup in Russia.
Laura Harvey
Harvey was yet another name associated with the manager's role and the former Arsenal boss further enhanced those rumours following her resignation as head coach of National Women's Soccer League team Seattle Reign at the end of last year.
The 37-year-old spent five years in charge of Seattle, after her highly successful career at Arsenal in which she guided the Gunners to 13 trophies during her spell. She carried that form to the US, where she won two NWSL shield titles and was twice awarded the NWSL Coach of The Year.
With such a pedigree, it was no surprise that Harvey was linked with the England job. But, while she was initially interested in having talks with the FA, it was fundamentally not the right time for the manager and at the end of November, she instead decided to sign with the NWSL's newest team, the Utah Royals.
Why was Mark Sampson sacked as England manager?
The former England boss was sacked in September of last year following an investigation into his conduct at Bristol Academy, the club Sampson managed from 2009 to 2013.
The Lionesses were led to a third-place finish at the 2015 Women's World Cup in Canada during his tenure - they were not only the most successful European team in the tournament but they also marked the best performance by any senior England team, since Sir Alf Ramsey's World Cup winning side of 66'.
And most recently England reached the semi-finals of the 2017 European Championships, only to be beaten by hosts and eventual winners the Netherlands.
However, following the success Sampson found himself embroiled in controversy. He was brought into the centre of a dispute with Chelsea and England striker Eniola Aluko, following allegations of discrimination and accusations of 'bullying and harassment'.
The 34-year-old denied the claims and was cleared of any wrongdoing following an internal investigation by the FA - with the governing body stating that Aluko's allegation was unrelated to Sampson's sacking.
An FA statement read: "In 2014, safeguarding allegations were made against him about his time with Bristol.
The safeguarding assessment was that he did not pose a risk working in the game."
"However, the full report of the investigation was only brought to the attention of the current FA leadership last week and it is our assessment that it revealed clear evidence of inappropriate and unacceptable behaviour by a coach. It is on the basis that we have acted quickly to agree a termination of Mark's contract."
England's current form
Whilst the FA continue negotiations for a new manager, England is currently second in their World Cup Qualifying group, a point behind leaders Wales with a game in hand.
Their next qualifier is against Wales in Southampton on April 6.
