As far as I am aware, yes koi and goldfish can live together.
But please be aware that koi need a lot of space, to keep koi you're talking a bare minimum pond size of 4546 litres or 1000 gallons, which would mean a large amount of filtration.
I would highly recommend reading this page as it covers the basics of having koi; (Link is not visible to guests. Please register to view.
Goldfish on their own however, as they don't grow as big as koi can inhabit smaller ponds, so a minimum pond size would be something around 1600 litres, with adequate filtration
Have you already got a pond -if so, how big is it i.e. dimensions and volume- or are you planning to build a pond?