Cristiano Ronaldo's scintillating form and the supporting role played by the likes of Gareth Bale and Karim Benzema suggest Real Madrid have every right to believe a rare treble is well within their grasp.
Barcelona became the only Spanish team to win the Champions League and the domestic league and Cup in the same season in 2009 and La Liga leaders Real are in a strong position to match their arch rivals after Ronaldo's goals helped them put together a 31-match unbeaten run since the end of October.
The Portugal forward has scored 41 in 37 appearances for the world's richest club this term.
His double in Tuesday's 3-1 win against Schalke 04, as Real secured their place in the Champions League quarter-finals with a club record 9-2 aggregate success, took his tally in the latest edition of Europe's elite club competition to 13.
His opening goal in the 21st minute showcased his ability to time his runs to perfection as he sprinted into the area and clipped a Bale centre into the net.
His second 17 minutes from time was classic Ronaldo as he collected the ball near the halfway line and charged past the helpless Schalke players before smashing a low shot into the bottom corner.
"Ronaldo didn't become World Player of the Year for nothing," Schalke coach Jens Keller told a news conference. "His qualities are outstanding."
With 13 goals in seven games, the 29-year-old former Manchester United player, who also scored twice in the 6-1 win at Schalke in their round of 16, first leg, has surpassed his best Champions League haul and is one short of the record of 14 set by Barca forward Lionel Messi in 2011-12.
"Cristiano is the best in the world," Real midfielder Casemiro, who had a rare chance to impress on Tuesday with his team virtually assured of going through, told reporters.
"He is a one-man show and an example for everyone," the 22-year-old added. "I learn a lot from him and he is an incredible player."
Real will find out on Friday who they will face in the quarter-finals and they could be drawn against Barca or city neighbours Atletico Madrid.
Real host Barca, the last team to beat them, in the La Liga "Clasico" on Sunday, when a win would stretch their lead over the champions to seven points and deal a severe blow to Barca's chances of a fifth title in six years.
Barca are third after a couple of surprise defeats, a point behind second-placed Atletico.
Barca and Real also meet in next month's King's Cup final, a repeat of the 2011 showpiece which Real won 1-0, raising the prospect of a possible four meetings between them in the space of just over three weeks.
Bale, who has started to come into form after an injury-disrupted start to his Real career, has developed a highly effective partnership with Ronaldo and the Wales winger said his confidence was high as the season enters a crucial phase.
"I am enjoying my game," he told reporters.
"We are playing well, with a lot of confidence, and are on a good run," he added.
"We are coming to a decisive part of the season and we have to keep it going.
"Barcelona is a direct rival and we will try to play a good match (on Sunday) and get the three points.
"They have very good players but we are focused on our game and on our team because we also have very good players."