The left-back, 23, says United have tracked him for a month and stepped up their interest in recent days.
Buttner came close to joining Southampton earlier this summer.
"One month ago Manchester United expressed their interest but in the last four days it became concrete," Buttner said.
"I have not spoken with [United manager] Sir Alex Ferguson yet, but if all goes well that will happen.
"If a week ago, you had told me that together with Robin van Persie I would be playing at Manchester United, I would have driven you straight to the mad house."
Ferguson has been in the market for cover for first-choice left-back Patrice Evra all summer after allowing Fabio to join QPR on loan for the season.
Buttner has spent his entire career at Vitesse and was included in the provisional Netherlands squad for Euro 2012.