The Bundesliga outfit are favourites to pick up their second Europa League Group G victory in Glasgow following their 2-1 home win over Hungarian side Ferencvaros on matchday one.
Postecoglou's side lost 4-3 to Real Betis in Spain in their opening fixture and go into the game on the back of a 1-1 home draw with Dundee United at the weekend which kept them in sixth place in the cinch Premiership, six points behind leaders Rangers, having collected 10 from seven matches.
The former Australia boss noted Leverkusen's strength, saying: "They are a side of great pedigree, they have outstanding individual players within their set-up.
"They are a fairly settled team, they haven't made a lot of changes from last year, so yes, they are a quality team, one of the best teams in Europe and they probably see themselves as a Champions League team.
"In terms of favourites in the group, Betis are a very good team, Ferencvaros gave Leverkusen a contest in the first game so that will bear out over time but no doubt they are a quality opponent, quality footballers and a challenge for us.
"We want to take it to them and they will certainly take it to us, we are going to get tested and hopefully it is a great game of football for our supporters to get excited about and hopefully we play our part in that."