The Dane had been among the names linked with the White Hart Lane vacancy following the dismissal of Andre Villas-Boas on Monday.
But Laudrup has made it clear he has no intention of leaving Swansea in the lurch in the middle of the season.
He said: "You can always look at things from different perspectives. The positive one is when your name is linked as someone thinks you are doing well. It is always positive and flattering when others are talking about you and your name is linked with other clubs and Tottenham is a big club.
"But I would never leave a club, not Swansea or anyone, in the middle of a season. I have never done that as a player or as a manager and I will not do it in the future."
Laudrup is preparing his side to face in-form Everton in Sunday's Barclays Premier League meeting at the Liberty Stadium.
Forward Michu is also a doubt. The Spaniard, who has six goals to his name this season, recently returned following an injury to his left ankle, but a long-standing problem with his right ankle is continuing to hinder him, much to his obvious frustration.
Laudrup admits the 27-year-old will need to undergo an operation to solve the issue, but is not sure as to when that will be with Michu still battling to be available against the Toffees.
"He will need an operation at some stage," said Laudrup. "In the best case it could be when he finishes his career. It could be at the end of the season, but it could be now.
"He has been struggling with his ankle as well as his knee. The professional he is, he wanted to play but in a lot of games he could not give 100 per cent.
"I said to him not to worry and just carry on but he wants to score goals and help the team.
"In the league he has not had the physical presence to do that and he has been worried about that.
"He is a very important player for us but if you are playing at 80 per cent then it is very frustrating and the performance is not what you wanted. It's been very frustrating for him.
"We have to be certain of what he needs to do and when, as the player always has the last word.
"If the player feels he is not even 90 per cent the final word will be his."
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