The Dane was linked with a number of high-profile jobs after guiding the Swans to Capital One Cup glory and a ninth-placed finish in the Barclays 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.
"Someone tried to know my availability through intermediaries, but there was nothing concrete," he said. "Also, I had given my word that I would be in Swansea."
Chelsea owner Roman Abramovich's first choice to succeed Roberto di Matteo last year was Pep Guardiola, who declined the Russian's offer in the midst of his year-long sabbatical in New York.
The former Barcelona coach then agreed to take over at Bayern Munich two months later.