Swansea will face the Hammers looking to record back-to-back wins for the first time in the Barclays Premier League this season, having enjoyed a handsome 4-0 victory over Sunderland last weekend.
On the face of it there would be little to suggest that Laudrup, a star for Juventus, Barcelona and Real Madrid and rated as one of the classiest players Europe has ever seen, would be an admirer of Allardyce and his more direct approach to the game.
But the Dane has been impressed by the clarity the former Bolton and Newcastle boss has shown in how he prepares his teams.
Laudrup said: "I like managers and teams who are very clear about what they want. There is not one truth in football. There is more than one way to play.
"People tend to think the winner is always right, but I always respect people who are very clear in what they want and what they are doing.
"There are some who say one thing and do another, but Sam Allardyce is very honest in what he wants and what he asks from his players.
"They are very strong and when we played them away last year they were very good so we know it will be difficult."
Swansea have a quick turnaround before facing the physical test the Londoners will provide, having drawn 1-1 with Kuban Krasnodar in the Europa League on Thursday.
The Swans were denied victory by a stoppage time penalty from Djibril Cisse after Michu had opened the scoring, although they still lead Group A by a point from Valencia.
Laudrup will be keen to end what he had dubbed a "huge" week for his side with a win, but pointed to West Ham's impressive recent win at Tottenham as proof of just how difficult it will be.
"I can't say we need to win it, we would like to win it," he said. "West Ham are a team at our level and we are at home and it's one of those where you can say we have a big chance to get points if we can.
"I have said before, and I stand by it, that this is a very important week for us.
"But the game against Kuban Krasnodar was in one competition and Sunday's is different. We will want a positive result on Sunday but it will be difficult as we will be playing a tough, very physical team in West Ham.
"We only have three days to prepare but we want to be in the Europa League and we know this is how it will be.
"They were a good team last year and when we played away they were very strong, physical and direct. They had Andy Carroll and Kevin Nolan up front.
"We know Carroll is not there for this game but we saw how strong they are the last time they played away against Tottenham, where they won 3-0. It will be tough."