The Baggies head coach was left fuming with skipper Jake Livermore after he was sent off in the derby loss to Villa.
His dismissal arrived despite Allardyce making it clear in his first training session following the sacking of Slaven Bilic that he will not tolerate any reckless red cards.
Speaking after that game, the Dudley-born chief confirmed he would assess his squad to see who wants to be captain for the three games Livermore will now be suspended for.
And he said if they did a good job, they could potentially keep the armband for the rest of the season.
As well as Livermore, vice-captain Kyle Bartley will also miss the Liverpool game on Sunday with a minor knock picked up in training.
And Allardyce wants complete honestly from whoever he does pick to wear the armband, with the boss preferring a player turned it down rather than let it affect his performance.
“There are different types of captains,” Allardyce said.
“There are captains that aren’t that vocal but lead by the way they perform.
“They are the consistently the best performers in the team – they lead by example.
“Then there are the ones who are consistent but who do a lot of organising and talking on the field.
“Having lost Jake – not only as an experienced Premier League footballer which we have few of here – we are losing our captain who in my short period of time seems to be communicating quite well on the pitch.
“We are going to have to have a really hard think who is going to be the captain for Liverpool and ask whether they feel comfortable with it.
“If they don’t feel comfortable with it I don’t want them to take it because we can’t afford anybody to off their game – not in any game, not just Liverpool. We need 100 per cent focus to get a result.”
Alongside Livermore and Bartley, Allardyce will also be without injured duo Sam Field and Hal Robson-Kanu for the trip to Anfield.
But he is able to call on Matheus Pereira – who is available once again having served a three-match suspension following his red card against Crystal Palace.
“Sam Field and Conor Townsend are still out,” Allardyce added.
“Hal Robson-Kanu and Kyle Bartley are still out.
“Jake Livermore, most disappointingly of all, is not available through suspension.
“But we do have Matheus Pereira back and I am looking forward to seeing him play because everyone keeps telling me he is one of our most talented players on the ball.
“We need to be able hold the ball and retain the ball more so I am looking forward to seeing him back in the squad.”