Manchester City will face Greek side Aris Thessaloniki in the first knock-out stages of the Europa League while Liverpool will take on Sparta Prague.
Both Premier League sides should be confident of making the last 16 following today's draw, but Rangers have a tougher-looking test against Sporting Lisbon.
Roberto Mancini's City will be aware however that Aris stunned the holders Atletico Madrid in the group stage - winning 3-2 away, a result which ultimately knocked the Spanish side out of the competition.
Liverpool may have been the draw specialists in the group phase, having tied four of their six games, but in Sparta they will face a side who have proved equally difficult to beat, having drawn three of their group matches.
If they get through, City will face Besiktas or Dynamo Kiev in the last 16, while Liverpool would face Lech Poznan or Braga. If Rangers progress, they would face Lille or PSV Eindhoven.
Aris' coach is the vastly-experienced Argentinian Hector Cuper, who like Mancini once managed Inter Milan.
Manchester City's football administrator Brian Marwood told Sky Sports News: "It's two former Inter Milan coaches going head to head and I'm looking forward to it.
"With the preparation time we have we feel we're in a very strong position in terms of our squad. Roberto has had the opportunity to rotate the group which allows players to be rested before certain games.
"It will be a difficult period, I think we play Manchester United before the away trip but as we get close we will prepare accordingly.
"The beauty of having a squad like ours, when we have important games, if we can stay clear of injuries and suspensions, we feel we're in good shape.
"You saw last night even with a lot of players who are not playing regularly, they were very sharp, very bright and there was a good intensity to the game."
Rangers beat Sporting Lisbon in the quarter-finals en route to the UEFA Cup final in 2008, clinched by a 2-0 win in Portugal.
Rangers manager Walter Smith told the club's website: "We know we will face two really tough games because they are playing well at the moment and we had to play well to win there last time out.
"We played some good football against them across the two legs and we will really have to repeat those kinds of levels to have success in the Europa League.
"Of course Pedro Mendes is there so we know the quality of player that we will face."
Steven Whittaker scored the second goal against Sporting in 2008 and he added: "There is no doubt that is the best I have scored, purely because of the importance of it and what it meant to the team.
"To see the ball hit the net was an unbelievable feeling, the best ever, and the atmosphere in the dressing room was fantastic."
The draw for the round of 32 in the Europa League is:
Napoli v Villarreal
Rangers v Sporting Lisbon
Sparta Prague v Liverpool
Anderlecht v Ajax
Lech Poznan v Braga
Besiktas v Dynamo Kiev
Basle v Spartak Moscow
Young Boys v Zenit St Petersburg
Aris Salonika v Manchester City
PAOK v CSKA Moscow
Sevilla v Porto
Rubin Kazan v FC Twente
Lille v PSV Eindhoven
Benfica v Stuttgart
BATE v Paris St Germain
Metalist Kharkiv v Bayer Leverkusen
The draw for the round of 16 in the Europa League is:
Benfica/Stuttgart v BATE/Paris St Germain
Besiktas/Dynamo Kiev v Aris Salonika/Manchester City
Rubin Kazan/FC Twente v Young Boys/Zenit St Petersburg
PAOK/CSKA Moscow v Sevilla/Porto
Lille/PSV v Rangers/Sporting Lisbon
Metalist Kharkiv/Bayer Leverkusen v Napoli v Villarreal
Anderlecht/Ajax v Basle/Spartak Moscow
Sparta Prague/Liverpool v Lech Poznan/Braga