The Hammers are the visitors to south London this weekend, with the Eagles still yet to appoint a successor to Tony Pulis, who left by mutual consent less than 48 hours before the start of the new Barclays Premier League season.
Former Cardiff boss Malky Mackay appeared a certainty to replace Pulis, with betting suspended on the 42-year-old, before it emerged he was at the centre of a Football Association investigation into his conduct during his time in charge of the Bluebirds.
It is understood that Palace's interest in Mackay is now over and, with former Tottenham head coach Tim Sherwood once again installed as favourite, Allardyce feels Eagles chairman Steve Parish should look closer to home
Millen, who guided Palace to one victory in a four-game spell following Ian Holloway's departure last year, oversaw an impressive display in a narrow 2-1 defeat at Arsenal last weekend.
Now Allardyce thinks it could be time for the former Bristol City manager to be entrusted with the position for a longer period.
"I think they need to appoint whoever the right man is as quickly as possible," he said.
"Keith, by his performance against Arsenal, he is a good stand-in and he has done it before
He was with them all season so that is fine, it might not be beyond the chairman of Crystal Palace letting him have a go.
"We have seen that happen before if he gets a few good results - it is a difficult situation to be in at the start of the season when you lose your manager but it is something you have to face and the players need to do their job and be professionals.
"They want guidance from the manager but for a short period of time they can use what they got through pre-season to go and get results."
West Ham take the short journey to Selhurst Park with both sides looking for their first win of the season having slipped to last-gasp defeats in their opening games.
Allardyce, who will be short of numbers in defence due to injury and suspension, wants his side to take advantage of any signs of instability shown by Palace's players on the pitch.
"I hope so," he replied when asked if the uncertainty over a new manager could see West Ham capitalise.
"I'm not sure sure because players are professional when it comes to changing managers, whether it is a surprise or it isn't.
"You only have to look at the way they played against Arsenal, in many ways they were unfortunate to lose a game away from home.
"They were suitably well organised and well drilled, they took that on the field from what Tony did over the period of time he was with them.
"They are always difficult to break down and we will find that to be the same, last year we found it difficult and lost both games 1-0."
Source : PA
Source: PA