The Dane was linked with a number of high-profile jobs after guiding the Welsh club to League Cup glory and a ninth-placed finish in the Premier League.
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 £2 million last summer.
The Spaniard has gone on to score 27 goals for the Swans and has been rewarded with his first call-up to the Spain squad for their World Cup qualifiers against Belarus and Georgia.
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."