Liverpool will face another side knocked out of the Champions League after being drawn against Unirea Urziceni in the last 32 of the Europa League today.
Rafael Benitez's side finished third in Group E while Unirea were third in Group G, despite recording a famous 4-1 victory over Rangers at Ibrox.
The Romanian champions also beat Sevilla 1-0 at home and are managed by former Chelsea defender Dan Petrescu.
Fulham will take on Ukrainian side Shakhtar Donetsk, the last team to win the UEFA Cup after beating Werder Bremen in the final earlier this year.
Everton will face Portuguese side Sporting Lisbon, who are currently seventh in the league, 12 points behind leaders Braga.
Liverpool legend Kenny Dalglish, in Nyon for the draw, is not under-estimating fellow Champions League drop-outs Unirea.
"I think they got eight points in their Champions League group which included Rangers, Sevilla and Stuttgart so that's a decent number of points.
"Obviously there is plenty of coverage now, it's not as if you're going to get a team that won't have been on television so there's plenty of tape there for Rafa (Benitez) to have a look at.
"And also there's a phone call up the road to Walter Smith at Rangers, I'm sure he'll be happy to disclose any information he's got on them.
"It will be a difficult game. They go on a break until March now but whether the rest helps them or hinders them remains to be seen."
Should they overcome Unirea, Liverpool will face Lille or Fenerbahce in the last 16 and Dalglish admits the Reds would relish a return to Istanbul, the city where they triumphed so dramatically in the 2005 Champions League final.
"We've got happy memories of Istanbul," he said. "But we've got to pay Unirea the respect they deserve.
Fulham's incentive against Shakhtar is a glamour tie for the winner against Ajax or Juventus in the next round, while Everton's last-16 opponents would be Atletico Madrid or Galatasaray should they beat Sporting.
In other last-32 ties, Athletic Bilbao meet Anderlecht, Marseille face FC Copenhagen, Roma take on Panathinaikos while there is a potentially explosive clash between Atletico Madrid and Galatasaray.
PSV Eindhoven were drawn against Hamburg, Villarreal and German champions Wolfsburg face off and Valencia meet Club Brugge.
Werder Bremen take on FC Twente and Hertha Berlin were paired with Benfica.
Europa League draw for the last 32 and last 16:
Rubin Kazan v Hapoel Tel Aviv
Athletic Bilbao v Anderlecht
FC Copenhagen v Marseille
Panathinaikos v Roma
Atletico Madrid v Galatasaray
Ajax v Juventus
Club Brugge v Valencia
Fulham v Shakhtar Donetsk
Liverpool v Unirea Urziceni
Hamburg v PSV Eindhoven
Standard Liege v Salzburg
Villarreal v Wolfsburg
FC Twente v Werder Bremen
Lille v Fenerbahce
Everton v Sporting Lisbon
Hertha Berlin v Benfica
First legs to be played on February 18. Second legs to be played on February 25.
Hamburg or PSV Eindhoven v Athletic Bilbao or Anderlecht
Rubin Kazan or Hapoel Tel Aviv v Villarreal or Wolfsburg
Atletico Madrid or Galatasaray v Everton or Sporting Lisbon
Hertha Berlin or Benfica v FC Copenhagen or Marseille
Panathinaikos or Roma v Standard Liege or Salzburg
Lille or Fenerbahce v Liverpool or Unirea Urziceni
Ajax or Juventus v Fulham or Shakhtar Donetsk
Club Brugge or Valencia v FC Twente or Werder Bremen
First legs to be played on March 11. Second legs to be played on March 18.
More to follow...Reuse content