The former France international left Bordeaux for Juventus in the summer of 1996 but was initially subject to interest from United at the time.
However, according to Edwards, Ferguson believed there was no room for Zidane and Cantona in his team and, as a result, opted against making a move for the 1998 World Cup winner.
Speaking to BBC Radio 5 Live, Edwards said: "Zidane and Eric played in the same position and Alex felt if they brought Zidane in it would have upset Eric.
"In hindsight yes [it's a regret], because Eric retired a year later and Zidane was younger so he would have continued it."
Zidane went on to spend five years in Turin after joining Juventus where he won two league titles, an Italian Cup and the Intertoto Cup.
He made the switch to Real Madrid in 2001, winning La Liga and the Champions League, before retiring in 2006.
The Frenchman returned to the Bernabeu in 2010 as a special adviser to Real Madrid’s first team.
He was later appointed as head coach of Los Blancos in 2016 with whom he has won back-to-back Champions League titles.