Former United skipper Roy Keane has emerged as one of the early favourites to take the Salford job.
Keane, 49, was pictured at Salford's Peninsula Stadium on Saturday, sat alongside Gary Neville and Scholes, as Salford drew 2-2 with Tranmere Rovers.
Bookmakers have Warren Joyce, currently boss of Salford's development squad, as favourite for the role, while former Wigan boss Paul Cook is also among the contenders.
Keane, who had spells in charge of Sunderland and Ipswich, is keen to return to management after working as assistant to former Republic of Ireland boss Martin O'Neill from 2013 to 2018.
He also had spells as an assistant boss at Aston Villa and Nottingham Forest.
Keane is currently working as a pundit for Sky Sports, but could make his long-awaited return to coaching with Salford, where he would be answerable to his former United team-mates.
Scholes has been put in temporary charge of Salford - until a permanent successor to Alexander is found - and will take charge of the team for Saturday's trip to Port Vale.
Scholes, co-owner of Salford with former team-mates Gary and Phil Neville, Ryan Giggs, David Beckham and Nicky Butt, was involved in the decision to sack Gary Alexander, who won just one of his last 10 home league games in 2020.
The 45-year-old will take his first training session on Tuesday, which will be captured on camera by the documentary crew filming the latest series of 'Out Of Their League', a behind-the-scenes look at the goings-on at the club.
Scholes has not been in management since his ill-fated short spell in charge of Oldham Athletic in March 2019, which lasted just 31 days.
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