Ferguson, a director at the Old Trafford club who hand-picked the former Everton boss as his successor last year, will be able to express his opinion along with every member of the Manchester United board.
And whoever takes over from Moyes will be given significant funds to rebuild the squad, sources said.
Holland coach Louis van Gaal emerged as the early front-runner to succeed Moyes, whose 10-month reign came to an end on Tuesday when he was fired following a meeting with vice-chairman Ed Woodward at Carrington.
It is understood that the United board first discussed the possibility of getting rid of Moyes on Sunday night following the team's 11th league defeat of the season at Everton.
On Monday the board, which includes Ferguson and Sir Bobby Charlton, decided Moyes should be sacked and he was summoned to the AON Training Complex the following morning to be dismissed.
Although Ferguson was responsible for appointing Moyes, he will play a part in choosing his compatriot's successor, although this time he will not be the sole man responsible.
United are looking to appoint an experienced manager who has a history of signing top-class players and managing them.
For that reason, the club are known to be interested in Van Gaal, who has won titles in Spain and Germany. The 62-year-old also won the Champions League with Ajax in 1995.
The Dutchman has made it clear he wants to move to England when his contract expires at the end of the World Cup.
Another potential candidate, according to reports, is Carlo Ancelotti, whose position at Real Madrid could be in jeopardy if the Italian fails to win either the Spanish league or the Champions League.
The United board will back their new manager in the transfer market, with the £150million kitty promised to Moyes still available.
Ryan Giggs will take care of the team "until a permanent appointment can be made", United said.
It is understood that Giggs will not be considered as a full-time replacement, but they hope United's most-decorated player will become part of the new manager's backroom staff.
For the final four games of the season, Giggs will be assisted by Nicky Butt, Phil Neville and Chris Woods - the latter two keeping their jobs despite being brought in by Moyes.
Steve Round and Jimmy Lumsden were also brought in by the Scot but they have been fired.
Moyes can have no qualms about his dismissal. This time last year United won the title with four games to spare. Now they sit 23 points below the summit in seventh place.
One United source said the board started worrying about Moyes' capabilities during the 2-0 defeat to Olympiacos.
"The players didn't look up for it," the source said. Once more "lacklustre" performances followed, the source added, Moyes had to go.
Fans and shareholders widely backed Moyes' dismissal, although former captain Roy Keane said the players should take a large portion of the blame.
"Some of the players should be ashamed of themselves," Keane told ITV1.
On Tuesday evening the club's share price on the New York Stock Exchange climbed sharply to its highest point since Ferguson's retirement last May.