The Dane has guided the Swans to seventh in the Barclays Premier League table on 26 points after their stunning 2-0 win over Arsenal at the Emirates Stadium last weekend. Michu grabbed both the goals to move to 10 for the season, putting him level with Luis Suarez, Robin van Persie and Demba Ba in the race for the golden boot.
The 26-year-old Spaniard has already been linked with some clubs in Italy, while Swansea fans have also become fearful that Laudrup could be lured away from the club. But Laudrup said: "We are here and we have to continue working. I am happy here and I think Michu is happy here as well. Why should we want to leave? We are not going anywhere."
The south Wales club have lost just one of their last 10 games in all competitions, a good run which started at a time when reports of dressing room unrest were appearing in the national media.
But Laudrup added: "There has been a lot said because everyone talks about Michu. I understand that because he is up there with Van Persie and Suarez and a lot of clubs would like to sign him.
"I don't want to let him go, sometimes the offer can be so big you have to accept but I really don't think clubs are going to pay so much money for him," said the Dane. "We have the example of what Liverpool paid for Joe Allen (£15million), if they have to pay double for Michu there are few clubs who could afford that.
"Joe went to Liverpool and you know more or less what they paid for him, but a guy who has scored many goals must be worth a lot more, so you work out the figures. I don't think anyone will come with that money so he will stay here."
Laudrup appreciates speculation over himself and Michu has arisen thanks to an excellent run which has included victories over Arsenal, Newcastle and West Brom, as well as draws with Chelsea and Liverpool.
But the Dane does not want the increased attention to distract his squad over one of the busiest periods of the season. He said: "If we lose focus in two or three weeks everything can change. We have already had that this season, we played great in the first two or three games and then we had three losses and it was another situation.
"We still have six games left this month, five of them in the league, that's 15 points so imagine what can happen."