According to the draw rules, Barcelona and Liverpool will meet with the playoff results in positions 15,16,17 and 18. If in the draw PSG meets Monaco then Benfica automatically meets Brest, or vice versa. The results of these 2 playoff matches will determine the potential opponents for Barcelona and Liverpool.
It should be underlined that Barcelona and Liverpool are the top 1 and 2 seeded teams, so these two teams are unlikely to face each other except in the Final.

Inter and Arsenal will also not face each other directly, because according to the UCL Play-off draw rules, the 16 teams that finish in the play-off round will be divided into 4 groups. So the possible opponents that Arsenal and Inter will face are Milan, PSV, Feyenoord or Juventus.
Here is a detailed review to make it easier to understand which teams will face each other in the next round.