Liverpool have drawn Manchester United in the last 16 of the Europa League following Friday’s draw, while Spurs will face Borussia Dortmund.
The two sides – the fiercest of rivals in England – have never faced each other in Europe before.
United have won all four of their meetings under Louis van Gaal’s management.
Liverpool will host the first leg at Anfield with Old Trafford staging the return after both sides came through their round-of-32 ties on Thursday night.
Tottenham, the third Premier League club in the draw, have been handed a tough test as they face Klopp’s former side Borussia Dortmund while Gary Neville’s Valencia have an all-Spanish tie having been drawn against Athletic Bilbao.
The ties will be played on March 10 and March 17.
Shakhtar Donetsk v Anderlecht
FC Basel v Sevilla
Villarreal vs Bayer Leverkusen
Athletic Bilbao vs Valencia
Liverpool v Man United
Lazio v Sparta Prague
Borussia Dortmund v Tottenham
Fenerbahce v Braga