Athletic defeated Rangers 2-0 last night to set-up a Europa League semifinal against United.
Williams and Oihan Sancet struck the goals for Athletic and the former said at the final whistle: "It's a dream to play at Old Trafford, it's an amazing stadium.
"We have to play a good match at home and then go there for the second leg, and hopefully reach that final. United are a great team and they showed that today with their comeback, but we're going to go there with ambition."
On the victory at San Mames, Williams continued: "I think the team is doing something extraordinary.
"Last year we won the Copa del Rey and this year we've made it to the Europa League semi-finals. I hope we can reach that final, the team is doing everything necessary to get to that potential final.
"We're happy, but we have to keep pushing, and that's the only goal we have."
Williams also had a word for fellow goalscorer Sancet, who converted from the spot to ease home nerves.
Nico added, "Oihan is an incredible player, sharing a locker room with him is a blessing. We have one of the best takers that the Athletic has ever had, and I am very proud of him."