Kawashima has been a regular starter for his country since the 2010 World Cup but says his decision over a new club would probably depend on guarantees of first-team football.
Kawashima said: "Talks are still going on [with West Brom] and we are waiting for people to start moving.
"I am talking with my agent but I am not in a rush. I will wait until the middle of June or something.
"I am talking with a few clubs but I have to look at the conditions, whether I can play or not and what the club are thinking. Then I will take my direction for next season."