Swansea boss Brendan Rodgers has confirmed that the club have agreed a fee of £1.5million for Vorm.
The goalkeeper, who is in the Dutch squad for their midweek friendly against England at Wembley, is in the final year of his contract with Utrecht.
"We have agreed a fee, obviously personal terms are till to be agreed," Rodgers said.
"It happened last night and we hope he is a player we can get an agreement on."
Should Vorm, 27, complete his switch to south Wales he will be Rodgers' sixth summer signing as the club prepare for their maiden Premier League campaign.
Rodgers, who saw his side beat Real Betis 1-0 in their final pre-season friendly at the Liberty Stadium today, added: "He is the Dutch number two and I think it says it all that we can attract that calibre of player here. He fits our style which is why it's taken so long for us to get the right type of goalkeeper.
"If we end up doing the deal that gets Michel in then it would be a wonderful signing for the club.
"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.
"I believe his agent was here discussing (the move) with the chairman and we hope we can get that complete in the next few days."