Chelsea defender Anita Asante in Neville's first squad, with the Chelsea defender called up for the first time since 2015.
Defender Stoney made her debut in 2000 and was capped 130 times, scoring six goals.
Brighton and West Ham will apply to have their women's teams join the restructured Women's Super League (WSL) in 2018-19, according to ESPN sources.
Arsenal boss Arsene Wenger believes that there will be a female manager in the Premier League sooner rather than later.
Football Association chief executive Martin Glenn is confident that Manchester United will eventually launch a women's team.
Liverpool Ladies extended their lead at the top of the Women's Super League Spring Series despite being held to a 1-1 draw at Bristol City.