Swansea, who had a reported £6m bid accepted for Ki, are expected to finally wrap up the signing before the weekend.
"He's an important player to have in midfield," Laudrup told BBC Sport. "We lost Joe Allen of course so it's important looking at the strength of the squad and to have a dynamic player like that.
"The players we have signed here and the players we will sign are players that can fit into our style.
"He's already played a couple of seasons in British football and that's very important. The players who have come in from abroad have had a great start but I think experience of this kind of football is important as well."
Ki has scored 11 goals in all competitions for Celtic since signing in 2010.