Buttner, 23, would become United's second recent Dutch acquisition following Robin van Persie's move from Arsenal to Old Trafford last week.
The player, who had been linked with possible moves to Queens Park Rangers, Fulham and Southampton, told reporters before leaving Schipol Airport in Amsterdam for Manchester that he was hoping the United deal would be completed soon.
"If a week ago, you told me that together with Robin van Persie I would be playing at Manchester United, I would have driven you straight to the madhouse," he said.
"One month ago Manchester United sent an email expressing their interest, but in the last four days it became concrete.
"I have not spoken yet with Sir Alex Ferguson, but if all goes well that will happen."
Buttner was included in a provisional Netherlands squad for Euro 2012, but did not make the final 23. He has made 107 appearances for Arnhem, scoring 10 times.