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.
"It would cause huge damage because if you lose players of that quality you have to find replacements of the same level," he said.
"That is why we cannot do that so late. If you sell someone and then try to buy, people know you have a lot of money.
"The price for the replacement would automatically go higher and higher, that's inevitable."
Laudrup has made eight new signings over the summer, most notably the £12million signing of Vitesse Arnhem striker Wilfried Bony and the capture of Liverpool midfielder Jonjo Shelvey for £5million.
Laudrup also admitted he is unhappy the summer transfer window remains open once the season has begun.
"It's part of the game and as long as the rules are like that we get on with it," he added.
"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."