Three of Europe's storied clubs are on the brink of Champions League elimination

Liverpool's Mohamed Salah during a training session at the AXA Training Centre, Liverpool, England, ahead of Tuesday's Champions League soccer match against PSG.( AP)

MANCHESTER, England, April 13 (AP): Three of European soccer's most storied clubs stand on the brink of Champions League elimination.

Real Madrid, Liverpool, and Barcelona must all overturn first-leg defeats in this week's quarterfinals.

Between them, they have won European club soccer's greatest prize 26 times. But they have left themselves with mountains to climb to advance to the semifinals.

Record 15-time champion Madrid trails 2-1 to Bayern Munich after a home defeat in last week's first leg at the Bernabeu.

Liverpool is 2-0 down to defending champion Paris Saint-Germain ahead of Tuesday's return match at Anfield, and Barcelona suffered a shock 2-0 home loss to Atletico Madrid at the Nou Camp.

In the other quarterfinal, Arsenal leads Sporting Lisbon 1-0 going into Wednesday's match at the Emirates.

Trailing leader Barcelona by nine points in the Spanish league, Madrid's best chance of success this season may be in the competition that defines it - the Champions League.

But it faces a major challenge to overturn its tie against Bayern in Munich on Wednesday.

The German giant has been one of the standout teams in Europe this season - finishing second in the league phase with seven wins from eight games and routing Atalanta 10-2 on aggregate in the round of 16.

Bayern has won 39 of its 45 games in all competitions this season - losing just twice. Vincent Kompany's team looks well-placed to win a seventh European Cup, which would see it move level with AC Milan as the second most successful team in the competition's history.

In Harry Kane, Michael Olise, and Luis Diaz, Bayern has one of the most lethal attacks in Europe, but had to rely on the enduring brilliance of 40-year-old goalkeeper Manuel Neuer to keep Madrid at bay in the first leg.

That should serve as encouragement for Madrid that it managed to create so many chances against Bayern's defense, but it will have to find a way past Neuer to avoid elimination.

PSG put an end to Liverpool's Champions League campaign last season and looks primed to repeat the act this year.

The first-leg win in Paris last week did not reflect the superiority of Luis Enrique's team on the night, which had a host of chances to rack up an even more commanding lead.

"Paris Saint-Germain was the better team, but we didn’t give up, and that’s why we have a chance now still in this tie, because they kept us alive by not scoring a few open chances,” Liverpool coach Arne Slot said.

Six-time champion Liverpool will be relying on the famous Anfield crowd to try to inspire another famous comeback in the fashion of its 4-0 win against Barcelona in 2019 after losing the first leg 3-0.