Laudrup: Chelsea enquired after me
A falling out between Swansea and Laudrup's agent Bayram Tutumlu over proposed transfer targets only added to the speculation, but the former Getafe and Real Mallorca boss ended up staying in south Wales.
But, quoted in A Bola, Laudrup claimed there was interest from Stamford Bridge before Mourinho signed on for a second spell.
He said: "Someone tried to know my availability through intermediaries, but there was nothing concrete.
"Also, I had given my word that I would be in Swansea."
Chelsea were unavailable for comment when contacted by Press Association Sport.
Arguably Laudrup's most important act as Swansea boss was completing the signing of Michu for just over £2million last summer.
The 27-year-old placed on record his thanks for Laudrup, telling the club's official website: "It's because of Michael Laudrup that I am here.
"He is one of the best managers I have ever worked with in my life."
He also revealed Chelsea midfielder Juan Mata has been helping him adjust to life in the squad.
"I feel like I am annoying Juan Mata as I am always asking him about the training and the new experience," he said.
"Mata is helping me a lot, I know him very well. I can't describe the feeling when I went into the pitch wearing the shirt of the best team of the world.
"But it is very easy to play with all these players. The players who are in the squad are the best in the world and they're at the maximum level."
Swansea have also given a first professional deal to Pau Morer. The 18-year-old Spanish midfielder has been training with the club's Under-21s since July, but could not sign professionally until his 18th birthday.