The Spanish defender is confident that his side can win the double this campaign but anticipates a tough match against Valencia in this weekend's Liga fixture
The Santiago Bernabeu club are in pole position to lift their first league crown since 2007-08 as they sit six points clear at the top of the table, and they will face Bayern Munich for a place in the Champions League decider.
"We are very ambitious and we to win the title in the two competitions we are in, La Liga and the Champions League," Albiol told bwin.com.
"One last effort from everyone and perhaps we can do it.
"The atmosphere in the dressing room is fantastic, we all get along with each other. You can see it on the field."
Looking ahead to Sunday's visit of Valencia, Albiol admitted that Madrid face a difficult task against Unai Emery's men, who sit third in the Liga standings.
"The most important thing is that we get the three points and have a good match in front of our fans," the 26-year-old added.
"It will be a very tough match because Valencia did not win their last three league matches and they will want to keep third place.
"We have to collect three points every game. There are still many matches remaining and, for now, we only have to think about the match against Valencia."