Arsene Wenger has been considering a move for the 22-goal striker having grown increasingly frustrated in his attempts to lure Liverpool's Luis Suarez away from Anfield.
As a result, the French tactician is scouring the market for alternative targets as he looks to strengthen his forward line.
Michu was one of the names on Wenger's hit-list, with the 27-year-old Spaniard having caught the eye off the back of a magnificent debut season in the Premier League.
Having signed for just £2.2 million from Rayo Vallecano last summer, Michu went on to lead the club's scoring charts, earning himself a new and improved four-year contract in January.
And Laudrup has warned that even a "ridiculous" offer would not be enough to tempt Swansea into parting with their star striker, leaving Arsenal running out of options as they look to improve their squad ahead of the new season.
"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."
Laudrup believes that selling Michu would put Swansea's Premier League status at risk, and believes losing their prized possession would not be worth it, whatever the bid.
"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'."
Swansea kick off their Premier League season at home to David Moyes' Manchester United on Saturday evening, where Michu is expected to feature alongside summer signing, Wilfried Bony.
Arsenal meanwhile, are to return to the drawing board as they look to bring in attacking reinforcements.
One name that has been mentioned is Manchester City's Edin Dzeko, whose future remains unclear following the arrivals of Alvaro Negredo and Stevan Jovetic - a former Arsenal target, no less.