Laudrup is determined to hang onto the pair and fears the club would struggle to find suitable replacements before the end of the transfer window if they were to let them go.
He said: "It would do huge damage if we lose players of the quality of Michu and Ashley because we have to find replacements at the same level and we cannot do that too late.
"Because if I sell someone and try to buy someone else the next day, the price of your replacement goes higher, it's inevitable.
"But it's very close to this club's deadline as far as selling anybody goes."
Laudrup has made eight new signings over the summer, most notably the £12m signing of Vitesse Arnhem striker Wilfried Bony and the capture of Liverpool midfielder Jonjo Shelvey for £5m.
The Dane, who is preparing his side to face Romania's Petrolul Ploiesti in the play-off round of the Europa League, has joined the growing list of Premier League managers calling for the transfer window to close prior to the start of the season.
Newcastle manager Alan Pardew and Chelsea's Jose Mourinho earlier this week stated their wish for managers to be able to start the season with a finalised squad, and Laudrup cannot understand why such a move would not have wholesale backing.
"It's part of the game and as long as the rules are like that we get on with it," he said.
"I went to the Premier League managers' meeting last week and one of the questions asked was why we could not move the transfer deadline, what is the reason to have it close after we have started the season here and in Spain and Germany?
"The answer was that in the other big leagues there was not a lot of interest in moving it.
"I cannot understand why not, because every manager should be interested in having the deadline closed when they play the first game."
The Swans will be heavily fancied to book their place in the group stages of the Europa League, but Celtic's defeat against Kazhakstan side Shakhter Karagandy served as a further warning about the increasing quality of teams in eastern Europe.
Petrolul Ploiesti are managed by former Romania international Cosmin Contra, who played under Laudrup at Getafe.
And Laudrup is taking nothing for granted.
"It's a new game and a different competition, we just have to leave the Premier League to one side for this game.
"We have to approach it as just the first half of the game, it means getting a good result which would be a win and, even better, a clean sheet.
"After conceding four goals against United it is even more important to get a clean sheet.
"Winning 1-0 would be a good result, with 2-0 I would be even happier.
"This will be a tough game. We have watched their games against Vitesse Arnhem and they have some some good players so we have to be careful.
"They are not used to going into the group stages in Europe, but neither are Swansea so we are the same."