Manchester City won both of their Premier League ties with Tottenham last season and also beat Mauricio Pochettino's side at Wembley earlier in this campaign.
Manchester United's tie against Barcelona means interim manager Ole Gunnar Solskjaer will enjoy another trip to the Nou Camp, where he scored the winner in United's Champions League final win over Bayern Munich in 1999.
Best images from the Champions League
Best images from the Champions League
Liverpool defender Virgil Van Dijk, right, celebrates after scoring his side's second goal during the Champions League round of 16 second leg soccer match between Bayern Munich and Liverpool in Munich, Germany, Wednesday, March 13, 2019. (AP Photo/Matthias Schrader)
BARCELONA, SPAIN - MARCH 13: Gerard Pique of Barcelona celebrates as he scores his team's fourth goal during the UEFA Champions League Round of 16 Second Leg match between FC Barcelona and Olympique Lyonnais at Nou Camp on March 13, 2019 in Barcelona, Spain. (Photo by Maja Hitij/Getty Images)
PARIS, FRANCE - MARCH 06: Marcus Rashford of Manchester United celebrate his penalty shoot of the victory with teammattes during the UEFA Champions League Round of 16 Second Leg match between Paris Saint-Germain (PSG) and Manchester United at Parc des Princes on March 6, 2019 in Paris. (Photo by Xavier Laine/Getty Images)
Soccer Football - Champions League - Round of 16 Second Leg - Real Madrid v Ajax Amsterdam - Santiago Bernabeu, Madrid, Spain - March 5, 2019 Ajax's Lasse Schone scores their fourth goal REUTERS/Susana Vera TPX IMAGES OF THE DAY
TURIN, ITALY - MARCH 12: Juventus players celebrate the victory at the end of the UEFA Champions League Round of 16 Second Leg match between Juventus and Club de Atletico Madrid at Allianz Stadium on March 12, 2019 in Turin, . (Photo by Filippo Alfero - Juventus FC/Juventus FC via Getty Images)
12th March 2019, Allianz Stadium, Turin, Italy; UEFA Champions League football, round of 16th 2nd leg, Juventus versus Atletico Madrid; Juventus players celebrate after defeating Atletico Madrid with the result of 3-0 going through to the quarter finals (photo by Pierpaolo Piciucco/Action Plus via Getty Images)
BARCELONA, SPAIN - MARCH 13: Moussa Dembele of Lyon and Jordi Alba of Barcelona battle for possession during the UEFA Champions League Round of 16 Second Leg match between FC Barcelona and Olympique Lyonnais at Nou Camp on March 13, 2019 in Barcelona, . (Photo by Maja Hitij/Getty Images)
Lionel Messi (derecha), tras anotar un gol por el Barcelona, festeja con su compañero Luis Suárez en la vuelta de los octavos de final de la Liga de Campeones ante Lyon, el miércoles 13 de marzo de 2019, en el Camp Nou (AP Foto/Emilio Morenatti)
OLIMPICO STADIUM, ROME, LAZIO, ITALY - 2018/11/27: Real Madrid's Welsh forward Gareth Bale makes an heel shot during the UEFA Champions League football match AS Roma vs Real Madrid CF at the Olimpico Stadium.
Real Madrid won the match 2-0. (Photo by Carlo Hermann/KONTROLAB /LightRocket via Getty Images)
Real forward Lucas Vazquez, background, and Ajax's Nicolas Tagliafico challenge for the ball during the Champions League soccer match between Real Madrid and Ajax at the Santiago Bernabeu stadium in Madrid, Spain, Tuesday, March 5, 2019. (AP Photo/Manu Fernandez)
Roma midfielder Daniele De Rossi, center, jumps for the ball with Porto midfielder Hector Herrera, center right, during the Champions League round of 16, 2nd leg, soccer match between FC Porto and AS Roma at the Dragao stadium in Porto, Portugal, Wednesday, March 6, 2019. (AP Photo/Luis Vieira)
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The first legs of the quarter-finals will take place on April 9 and 10, with the second legs on April 16 and 17.