Amorim is facing pressure after a mixed start to the season, with Manchester United sitting 10th in the Premier League and eliminated from the EFL Cup after a loss to Grimsby Town.
Despite a recent win against Sunderland, Amorim's job is at risk if results don't improve. The club is looking for a new manager, and Keane and Scholes have shared their thoughts on who could take over.
Keane initially suggested Atletico Madrid manager Diego Simeone, who has never managed in the Premier League. Keane believes Simeone would bring a big personality and a winning attitude to the club.
"I think Simeone would rock up to Manchester United and say 'this is how you do things'. He's got a track record and a big personality. He'd create a bit of chaos, but it would be good chaos," Keane said.
However, Scholes disagrees and thinks Newcastle United manager Eddie Howe would be a better fit. Scholes has praised Howe's experience and ability to manage in the Premier League.
"Eddie Howe, Eddie Howe," Scholes said. "He's a good manager and I think he'd be a great choice for Manchester United."
Despite the speculation, Manchester United owner Sir Jim Ratcliffe has expressed his support for Amorim, saying he expects the manager to stay for at least three years.
Amorim will complete his first year as manager in November, and he'll continue to face pressure to deliver results and prove himself as a capable leader.