Former Juventus, Barcelona and Real Madrid star Laudrup was formally unveiled to the media after agreeing a two-year contract as Brendan Rodgers' successor.
And among the Dane's immediate priorities will be potential talks with 22-year-old Iceland international midfielder Sigurdsson, whose playing future appears to lie with either a permanent Swansea move or joining Rodgers at Liverpool.
The Swans last month agreed a £6.8million fee with German club Hoffenheim for Sigurdsson after a five-month loan spell in Wales won him numerous admirers.
Rodgers' recent move to Anfield, though, has put a spanner in the works from Swansea's perspective, and he remains a player in demand.
"It's a special case," Laudrup said.
"He was on loan here and did very well.
"As far as I know he has a possibility to go to another club. He is owned by a German club.
"I would like him to stay - he did very well here - but you have to look at a lot of things."
Laudrup has confirmed that Erik Larsen, his assistant manager when he was in charge of Real Mallorca, is set to join him in west Wales.
But he will also take stock of what is at his disposal player-wise before looking to strengthen a Swansea squad that coped admirably during last season's debut Premier League campaign when their scalps included champions Manchester City and Arsenal.
"I would like a new beginning, to come in and see how things are here," Laudrup added.
"But change for change's sake, I don't think that is good. To sign seven or eight players does not make sense," he added.
"It is a little early to talk about targets for next season. This is Swansea's second season in the Premier League - the first one was fantastic for them.
Watch: Laudrup attracted by Swansea philosophy.. More Videos
"It will be a huge challenge for me here, but also a great experience. When I heard about the interest, I had a lot of digging to see what kind of football Swansea play and what do they want to do.
"I saw that they try to have the philosophy that the chairman [Huw Jenkins] is talking about, which I think is going along with how I see football.
"That's one of the main reasons why I'm here because I think that is very important.
"It's the club, always the club, that points out the philosophy and then you have to pick the manager. But the manager also goes along with the way things are done.
"I didn't know so much (about Swansea), to be honest, but the people I talked to were very positive about the club. People said 'Michael, it would be a good club for you'."
Jenkins is understandably elated to have recruited Laudrup, who stands as one of Europe's finest-ever footballers as he prepares for a first tilt at Premier League football.
Jenkins said: "There is no doubt about his standing as one of the game's greatest footballers, but we also see the qualities he has as a manager.
"I am confident that Michael will prove a fantastic acquisition that will help keep this football club moving forward.
"We are delighted to have somebody with Michael's background. It's great for us as a club that Michael has joined us.
"The most important thing is finding the right person with the personality to forge the right sort of relationship.
"We are really looking forward to taking the club forward and carrying on the good work we have done in the last two years.
"We've always tried to deal with it in a common-sense way. Our remit every year is to make sure we are competitive.
"We will do everything we can to make sure we try to strengthen the team."