The Swans have agreed a fee of around ?6million with the Scottish champions for the South Korea international, who helped his country secure a bronze medal at the Olympics.
The 23-year-old is due to have his medical and finalise personal terms on his switch to south Wales.
Ki's agent admitted the player had been impressed by Swansea's opening day 5-0 trouncing of QPR last weekend, and Laudrup is looking forward to bringing in his seventh summer signing and strengthening his midfield following Joe Allen's departure to Liverpool.
He said: "The contract is not signed yet. I would like to wait before everything is signed and sealed but the deal should go through, he is an important player for us to have in the midfield.
"We have lost Joe Allen so it is important for the strength of the squad to have a player like that, if we sign him then we'll all be happy.
"He's a very dynamic player and, like the players we have signed and those we will sign, he can fit into our style. He has already played a couple of seasons in British football, which is important.
"The players we have brought in from abroad have made a great start, but to have experience of the British style of football is important."
Laudrup also remains interested in adding Valencia winger Pablo Hernandez to his squad. The Welsh club have had an initial bid of ?4million rejected by the Primera Division outfit, but they are likely to return with an improved offer after the player voiced his interest in a move.
"We still have eight days (to complete a deal)," said Laudrup. "It is always nice to hear players want to come here or play for a manager, but we will leave these things until after Saturday's game against West Ham because the most important players are the ones that are here, not the ones who could come or leave, that's why we must focus on the game."
Source: PA
Source: PA