Cillessen has been strongly linked with a move to Old Trafford as a replacement for David De Gea.
De Gea is trying to force through a move from United to Real Madrid before the transfer window closes.
But Cillessen insists that there has been no contact with United.
“As far as I know it has never been a thing,” he told NOS.
“I, the club, or my agent have never heard anything. As for me, this season begins and ends at Ajax.”
