Edwards, who had a spell as interim manager at Molineux in 2016 having previously made more than 100 appearances in old gold, has reportedly been in contact with the Gloucestershire side.
Talks are not thought to be at an advanced stage yet but the 38-year-old could replace Mark Cooper – sacked last month – at the New Lawn.
Edwards is now working for the Football Association, managing England Under-16s and helping out with the under-20s, having left Wolves in October 2019.
After progressing through the ranks at Villa, the ex-defender played 111 times in a four-year spell with Wolves before going on to retire through injury, aged 30.
He later joined Wolves as under-18s coach and was then promoted to the first team set-up in 2015.
In October 2016, Edwards had the role of caretaker manager – after the sacking of Walter Zenga – for two games, drawing 1-1 to Blackburn and losing 3-2 to Derby.
He left Wolves for the 2017/18 campaign and took charge of AFC Telford United, overseeing a 14th-place finish in National League North.
Edwards then returned to Molineux and led the under-23s to promotion to Premier League 2 Division One before leaving for the FA.
Forest Green currently have Jimmy Ball in caretaker charge and are in the final play-off spot in League Two ahead of Saturday’s final game of the season at Oldham.
It had previously been reported they were considering appointing the Football League’s first female manager.
Club chairman Dale Vince said: “I think we’ll take a new direction in our recruitment. Maybe we’ll break some new ground.
“We’ll recruit the kind of person perhaps that hasn’t been recruited before to be a head coach.”
And on if he could appoint a female coach, Vince added: “I don’t want to hint, but it could be. It is missing in men’s football, but so are BAME (Black, Asian and minority ethnic) head coaches.
“Everything is possible with us, because we don’t come at this in any preconceived way or in a way it has always been done.”