The 26-year-old forward netted his 19th goal of a superb debut campaign in English football, side-footing Swansea's second beyond Bradford keeper Matt Duke as part of an emphatic 5-0 Capital One Cup final triumph.
Laudrup continues to be linked with some of the biggest jobs on the continent, but Michu said: "The gaffer here has done great in his first season. But I have gone up to Michael and said 'stay with us now we are in Europe'."
He added: "I know other people will want him. He is really good, doing really well and maybe he can go with another club, but I hope he will stay here.
"We are growing up really fast and it is always difficult for a club of our size to win a trophy.
"But I think now we are going to play in Europe we can bring in some very good players and can be a stronger team next season."
Michu sympathised with Bradford as their hiding condemned them to the heaviest defeat suffered by any side in a League Cup final, but acknowledged the key moment of Swansea's route to Wembley had come in their 2-0 win at Stamford Bridge in the first leg of their semi-final against Chelsea.
He said: "We scored five, which is never easy to do.
"It was a great performance because Bradford have been very impressive in this competition.
"But the most important game for us was against Chelsea in the semi-final. We are here because of the way we played at Stamford Bridge."
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