Alex Ferguson's United completed a remarkable feat that season by picking up the Premier League title, the FA Cup and the UEFA Champions League, and Ferguson feels that his current squad contains enough quality to emulate that achievement.
The Red Devils mounted a strong challenge on three fronts last season, reclaiming the league title but eventually falling short in the semi-finals in Europe and the in the final of the FA Cup.
Ferguson feels that injuries to key players at vital times during the last campaign ruined their chances and is confident that as long as he can keep his strongest side fit this time around then they will be difficult to stop.
Possibility
"The Treble is achievable for us, there's no doubt about that" said the United boss.
"Last season I'm certain that if we'd had a stronger squad we could and would have done it but players like Gary Neville, Rio Ferdinand, Nemanja Vidic and Mikael Silvestre all got injured at a bad time.
"We didn't have an experienced central defensive pairing to go into the Champions League semi-final second leg against AC Milan, but we are stronger this time.
"We know it would be tremendously difficult for us, or any team, but if you are in the competitions then it is a possibility.
Luck
"But now we've got to concentrate on a tricky FA Cup tie against Tottenham then Lyon in the Champions League, so we have difficult games ahead.
"Like all managers I'm hoping to steer clear of any injuries for these tough games.
"In 1999 only Henning Berg missed the final through injury, everyone else was fit. That was a good break and you have to have that luck.
"If we get to the semi-final of the European Cup and the FA Cup and are still involved in the League this season then we must have some sort of a chance, it might not be a great one but it's some sort of chance."