Laudrup expects to bring in one striker on deadline day, having watched his side bank their first three points of the season with a 2-0 win at West Brom on Sunday.
The Dane admits he would rather have completed his summer signings before the last minute, but spoke calmly and condfidently about putting the finishing touch to his squad.
"We have to go into the last day having not done everything, which is not ideal because it will be a crazy day, but hopefully we'll finish in time," said Laudrup after goals from Ben Davies and Pablo Hernandez put the Baggies away.
"I've been asked about a lot of players and I've always said we want one more striker with different characteristics to Wilfried Bony and Michu. We will add one."
Albion's out-of-favour forward Peter Odemwingie is one of those linked to Swansea, but Laudrup would not be drawn on names.
"We've had five, six, seven players linked and one will join, but not more than one," he said.
"I don't want to go into details but let's say we hope to finish it as quickly as possible."