The 27-year-old has been named in the Holland squad for Wednesday's friendly against England.
"We have agreed a fee, obviously personal terms are still to be agreed," said manager Brendan Rodgers.
"It happened last night and we hope he is a player we can get an agreement on.
"He has experience and there are many terrific Dutch goalkeepers so for him to be number two and have that experience is a great coup for us," he added.
Swansea won their final friendly before their debut Premier League campaign with a 1-0 victory against Real Betis at the Liberty Stadium.