Laudrup and Pochettino are regarded as two of the most promising managers in the Barclays Premier League after flying starts to their respective careers in England.
Laudrup built on the solid foundations laid by Brendan Rodgers and Roberto Martinez to lead Swansea in to Europe following their Capital One Cup triumph.
And Pochettino has also taken Southampton on following the good work of Nigel Adkins, employing an attractive brand of football built around a good mix of foreign flair and home-grown talent.
Laudrup locked horns with Pochettino for two seasons during the 1990s, when they played for Real Madrid and Espanyol respectively.
There were little similarities between the two then.
"As players we were completely different," the Southampton manager said.
"He was a world-class striker and I was just a simple centre-half so we don't compare in that sense."
The similarities became apparent when their playing days came to an end.
Laudrup tried, with differing levels of success, to bring an attacking philosophy to Brondby, Getafe, Spartak Moscow and Mallorca when he went in to management.
Pochettino tried a similar tact at Espanyol, and now the coaches possess two of the most attractive teams in the Premier League.
Pochettino has been impressed by how Laudrup has taken Swansea on since he replaced Rodgers in the summer of 2012.
"With Swansea's last few managers, they have played, good attractive attacking football and Laudrup is no different," Pochettino said.
"He and I share a simple philosophy about how our teams want to play so we do have that in common.
"I am happy for him. Since I have come to England I have been able to see more of the work he has done there.
"He has done a great job."
Pochettino made it clear on Friday that he is not interested in the Europa League, but Swansea have enjoyed their time in the tournament.
The Welsh side gave their fans a memorable 3-0 win in Valencia last month and on Thursday they beat St Gallen 1-0 to move top of Europa League Group A.
Southampton have not played since last Saturday when they beat Crystal Palace 2-0, but Pochettino believes the extra few days' preparation will give his team no advantage.
"It won't give us the edge as they have time to recover, and they have a big squad with plenty of good players in it," he said.
"We expect to find a competitive Swansea, one that we will find it hard to break down.
"We hope it will be a good game."
Record signing Dani Osvaldo finally found the net for the first time last weekend on his fifth appearance for the club.
Pochettino, who managed Osvaldo at Espanyol, hopes the Italy striker can keep on scoring to help keep Saints up the top end of the table."
"The most important thing for a striker is always to score goals, that is what they need to do," he said.
"It's not just about playing well. The fact that he scored is going to make him much more relaxed and calm.
"That will help him to develop a lot more so that first goal was key for him."