United are currently top of the Premier League table with a game in hand on their main rivals, while they will face Tottenham in the final of the Carling Cup at the beginning of March.
Sir Alex Ferguson's men have also advanced to the last 16 of the UEFA Champions League and the FA Cup and Carrick accepts that it would be an incredible achievement to claim so much silverware.
However, the midfielder realises it will require a monumental effort if United are to succeed in their quest for an unprecedented quadruple.
"We will see whether it's possible to win the four - we will give it a good go, that's for sure," Carrick told the Sunday Mirror.
"At this club we want to win every game and we go into every game expecting to win, but it's tough to win all four competitions.
History"It hasn't been done, but this club is always making history and breaking new ground.
"It hasn't happened before because so many things can go wrong.
"It's difficult, especially in cup competitions because one slip and you can be out."
United face Derby in the FA Cup on Sunday and Carrick insists there will be no complacency, following last season's surprise defeat to eventual winners Portsmouth.
"We look back at that game (against Portsmouth) and know if we had won it we might have won the treble," said Carrick.
"That's why this season we don't want to finish with any regrets that we might have done better."