Barca take on Slovakia's Puchov at the Nou Camp after being held to a 1-1 draw in the first leg of their first round clash.
That result, coupled with Barcelona's failure to win at home this season, has put pressure on coach Frank Rijkaard, who has called for patience from the club's discontented fans after his side's slow start.
The Catalans were jeered by sections of their home crowd following a 1-0 defeat by Primera Liga leaders Valencia on October 5, and any slip-up against Puchov is sure to undermine Rijkaard's position.
Brazilian forward Ronaldinho is a doubt for the game after suffering a leg strain in a King's Cup match earlier this month.
Liverpool, UEFA Cup winners in 2001, welcome Slovenia's Olimpija to Anfield after a Michael Owen goal secured a 1-1 draw in the first leg where they had fallen behind to an Anton Zlogar strike.
Gerard Houllier's side must shake off recent poor league form having lost their last two games to sit in eighth place, nine points behind leaders Arsenal after eight games.
CONFIDENT PARMA
Parma, UEFA Cup winners in 1995 and 1999, also drew their first leg 1-1
Roma, third in Serie A, should breeze through after hammering Vardar Skopje 4-0 in the first leg, while fellow Italians Perugia and Udinese will expect to join them after picking up away wins at Dundee and Salzburg respectively.
Three German sides will have to improve on their first-leg performances to reach the second round.
The 1997 winners Schalke start all-square with Kamen Ingrad after a goalless draw in Croatia, while Hertha Berlin visit Poland's Groclin Grodzisk, also after a 0-0 first-leg result.
Kaiserslautern, 13th in the 18-team Bundesliga after having three points deducted before the start of the season for breaching licensing rules, travel to the Czech Republic needing to overturn a 2-1 deficit against Teplice.
The pressure is on coach Erik Gerets, who said he feared that the four-times German champions, after battling against relegation and financial collapse last season, would continue to struggle following their first-leg defeat.