"Wouldn't it be great," said Ashbee. "Leading Hull out at Roma.
"It would not be so much the icing on the cake as the hundreds and thousands on top of that.
"We know what we are trying to achieve, but if we keep winning football matches - I know there are going to be losses along the way - you never know.
"If you had asked me five years ago when I was leading the side out in League Two if we would be playing against Manchester United and Chelsea, I would have said no. So Europe is something I would never say no to."