The Dane's future has been a hot topic after an impressive debut season in which he masterminded a ninth-placed finish and Capital One Cup glory - the first major trophy in the club's history.
Paris Saint-Germain and Monaco were reported summer suitors but though Laudrup refused to talk specifics, he admitted he had rejected high-profile approaches to stay in south Wales for at least another season.
"I've never been close to leaving because I said I would stay this season; it's important to us," Laudrup told Sky Sports News.
"We still have to consolidate this team, this club and a promise is a promise - that's why I'm here.
"Yes, it's true, there were some approaches from big clubs as well, even from Champions League clubs, but I said I was going to stay here."
Laudrup had warned Swansea chiefs the club would have to strengthen to build on last season's success.
And he has signed seven new players - including striker Wilfried Bony for a club-record £12million fee - as well as securing the stay of Villareal midfielder Jonathan de Guzman on a season-long loan.