Giggs said: “Having tasted victory in 1999, it’s a burning desire of mine to win the European Cup again.
“I saw what it meant to the fans and what it did in terms of recognition for United, and I want to experience it again.
“If I retired having won just the one Champions League, I’d be really disappointed. To go for seven or eight years after that 1999 win and not match that night ever again would be a real let-down.
“I only say that because over that period United have had teams that have been capable. I’ve been lucky enough to have won almost every major trophy more than once.
“The European Cup is the exception to that, so I’m determined to do it. I’ve maybe only got a year or two left. That’s driving me on.
“I can see the finishing line and I’m just trying to enjoy it. Sometimes when you see the finishing line you tend to enjoy it more and it brings out the best in you.”
He added: “The potential is there in this team, but we have to fulfil that potential by winning trophies.
“We’ve got ourselves in a great position this season, going for three trophies, so hopefully we can go all the way and win them.
“Each challenge that has been put in front of this team this season, we’ve overcome.
“We’re getting results, even when we sometimes have to grind them out.
“We’ve got results when we’ve not been playing well this season, which has been crucial.
“Wayne and Cristiano are getting better each week, and as individuals they want success themselves against the best in Europe, and we have a chance to do that against Roma.”