Laudrup, 48, was talking the day after Premier League Swansea won the first major title in their 100-year history by crushing fourth tier Bradford City by a record 5-0 scoreline in the League Cup final at Wembley.
"I've said I'd like to stay here but even if you have a 10-year deal, there will always be rumours.
"My intention is to stay here next year, that's the only thing I can say really," the Dane, who previously managed Getafe and Real Mallorca in Spain, told Sky Sports.
"I am proud of that because there were 40,000 voters and it's 78 percent in front of two huge names like Rafael Benitez and Carlo Ancelotti, who have won league titles in Italy and Spain and the Champions League. So I'm very grateful," he said.
"But I can't really say anything more. There will always be rumours but this time it's positive rumours about one club or another club.
"I can only sustain what I've said before - my intention is to stay here, I have one more year on my contract. And that's it."
Swansea, who have secured a place in the qualifying rounds of next season's Europa League, are also chasing a top-half finish in the Premier League and have been widely applauded this season for their attractive passing game which Laudrup maintained after taking over from Brendan Rodgers when he moved to Liverpool last year.
