The 28-year-old's Belgian club Lierse SK say they have received an initial bid and a deal appears likely.
Kawashima said: 'Talks are still going on [with West Brom] and we are waiting for people to start moving.
England bound: Eiji Kawashima looks set for a move to West Brom
'I am talking with my agent but I am not in a rush. I will wait until the middle of June or something.
'Iam 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.'
Albion's 14-year-old midfielder Jerome Sinclair is wanted by Liverpool.
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