Koeman's side put out Arsenal in the first knockout round in March and last season, when he was in charge of Portugal's Benfica, he outwitted Liverpool counterpart Rafael Benitez at the same stage to knock out the then defending champions.
Koeman's Benfica also consigned Manchester United to bottom place in their group last season with a 2-1 home victory.
PSV are riddled with injury problems, however, for the visit of a Liverpool side who looked in fine fettle when beating Arsenal 4-1 on Saturday to go third in the Premier League.
Towering Brazilian defender Alex, whose header knocked Arsenal out at The Emirates Stadium, is sidelined by injury while Ivorian striker Arouna Kone suffered a knee injury in that game and has not played since.
Youngster Ibrahim Afellay, capped for the first time by the Netherlands last week, is also struggling to recover from a hamstring injury picked up during Saturday's 1-1 draw at NAC Breda -- a result that meant PSV's lead in Dutch league was trimmed to two points.
"We don't have the fittest squad at this moment," said Koeman, "but we will not give up despite two matches against Liverpool in a week.
"Afellay is a major doubt. We have problems battling for silverware on two fronts."
Former Dutch international striker Patrick Kluivert played against NAC, and could get a rare Champions League outing against Liverpool.
Liverpool and PSV have already met twice in this season's competition, Liverpool posting a psychological advantage with a 2-0 victory at Anfield and a 0-0 draw away in the group phase.
PSV will be wary of the threat of Peter Crouch on Tuesday.
The lanky England international scored in the 2-0 victory over PSV in November and was in sparkling form when he notched a hat-trick against Arsenal on Saturday after returning from surgery on his nose.
"Crouch hadn't played for 20 days because of his nose operation and he was desperate to play and score goals," Benitez said after the Arsenal win, hinting that Crouch may get the nod to start against PSV.
"All of his goals were fantastic. Xabi Alonso and Javier Mascherano controlled the midfield and it has set us up nicely for the Champions League against PSV Eindhoven."
Liverpool have proved a tough nut to crack in Europe this season, losing just one match away to Galatasaray when progress to the knockout phase was already assured.
Benitez confirmed on Sunday that captain Steven Gerrard, substituted against Arsenal, would be fit, saying the midfielder was simply tired after international duty.
PSV: 1-Gomes; 2-Jan Kromkamp, 14-Manuel da Costa, 13-Alcides, 23-Carlos Salcido; 20-Ibrahim Afellay, 11-Edison Mendes, 6-Timmy Simons, 8-Phillip Cocu; 17-Jefferson Farfan, 9-Patrick Kluivert
Liverpool: 25-Pepe Reina; 3-Steve Finnan, 23-Jamie Carragher, 5-Daniel Agger, 2-Alvaro Arbeloa; 16-Jermaine Pennant, 8-Steven Gerrard, 14-Xabi Alonso, 6-John Arne Riise; 15-Peter Crouch, 17-Dirk Kuyt
Referee: Bertrand Layec (France) (Additional reporting by Martyn Herman, London)