The outcome, which was recorded by Spanish newspaper AS, showed that three out of four of the 32,000 supporters that took part want the Dane to replace Jose Mourinho at the end of the season.
Despite insisting that he intends to stay with League Cup winners Swansea for at least another season, the 48-year-old conceded that he cannot stop the "rumours".
"I am proud of that. I'm in front of two huge names like Rafael Benitez and Carlo Ancelotti," he told Sky Sports News. "I can't really say anything more. My intention is to stay here and I have one more year left on my contract.
"I'd like to stay here but even if you have a 10-year deal there will always be rumours."
Laudrup had a two-year playing stint with Madrid up until 1996.