The Gunners have so far been frustrated in their efforts to bring in Luis Suarez from Liverpool and are reportedly considering alternatives as Arsene Wenger looks to bolster his forward options.
Michu is thought to be one of those alternatives after the 27-year-old Spaniard enjoyed a stunning first season in English football with the Swans, scoring 22 goals after his £2.2million move from Rayo Vallecano.
Michu signed a four-year contract with the Swans in January, and Laudrup has previously stated he values the forward at least £30million.
And the Dane has told Arsenal there is no way Swansea will sell a key player when they would themselves be left with so little time to replace him.
"I think economically the club is very good," said Laudrup. "I know if they (Arsenal) came in with a very late bid, I know that the reaction from the board and chairman will be 'No', even if the money is ridiculous, as we will not have time enough to find a replacement who is near enough to the same standard.
"You can say we would get a lot of money but why be the richest club in the championship? What is that worth?
"I spoke to Michu last year and he extended his contract and asked me about mine and I said 'I am going to stay here', and he said, 'So am I'."
Laudrup has looked to ease the burden on Michu this season with the signing of Wilfried Bony for a club-record fee of £12million from Vitesse Arnhem.
Bony's arrival has allowed Michu to move back into his preferred attacking midfield role, and Laudrup expects him to weigh in with another healthy goalscoring tally this season.
He said: "Michu is an offensive midfielder who can play centre-forward but he will be a goalscorer wherever he plays.
"He is not only a goalscorer who is up there, waiting. When he plays in midfield he is working very hard and physically he has a presence and fills a lot of space as well.
"I see him more as an offensive midfielder. He can come in from that second line where he is so gifted.
"Of his 22 goals last season, I think 20 of his goals were first touch which shows how effective he is."