That is according to Stoke midfielder Charlie Adam, who was appearing as a pundit on BBC Radio 5 Live tonight.
Aston Villa tonight announced the appointment of Dean Smith, who leaves fellow Championship side Brentford.
Arsenal legend Thierry Henry was the early favourite but he ruled himself out of the running earlier this week.
John Terry, who spent last season as a player at Villa, will be Smith’s assistant at Villa Park.
Former Manchester United assistant Rui Faria emerged as a candidate earlier today but quickly turned down the job.
And in a sharp turn of events, Smith has been given the job at the club he has supported since he was a boy, leaving Brentford after three years.
But, before hearing the news, Adam believes either Allardyce or Moyes would have been the better option in attempting to gain promotion to the Premier League.
“If I’m Aston Villa, I’m going for the quick fix now,” Adam said.
“The quick fix is your usual suspects.
“Yes Dean Smith’s going to have a chance because he plays good (football).
“But Sam, David Moyes, they’re going to get linked.
“They’re probably their best options if they want that fix now and get back in the Premier League.”
Meanwhile, former Villa striker Dwight Yorke believes he should have been given a shot at the vacant manager’s job.
“For me, I know Villa inside and out, what the youth system is about,” he told talkSPORT.
“I felt after Brucey was not able to advance them further they need someone with an inside knowledge of the club, who is passionate, who is going into management for the first time, who is exciting, who is trying to play attacking football, who won the league with Roy Keane.
“I’ve got the CV. Villa need to think outside the box. Why not? I’ve seen (Steven) Gerrard, (Frank) Lampard, Joey Barton, Lee Bowyer (get jobs in management), what have they got that I haven’t got?”