The first leg of the quarterfinals are to be played on April 11 followed by the second leg a week later on April 18.
Having guided United past Paris Saint-Germain in stunning fashion, Ole Gunnar Solskjaer must now mastermind a quarter-final win over Barcelona, meaning a return to the Nou Camp 20 years after his Champions League final victor there against Bayern Munich.
Unai Emery will not care though and he said after the game that he is "proud" of his players.
Prior to the Gunners' victory, Chelsea completed their progression to the last eight of this season's Europa League, which was done in style with a convincing 5-0 thrashing of Dynamo Kyiv.
Arsene Wenger is backing Arsenal to reach the Europa League semi-finals at the expense of Napoli next month.
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"It is not all like we wanted with the control, but I think as a competitive match, we did very well".
Arsenal take on a Napoli side who narrowly missed out on qualification from the Champions League group stage after finishing third behind Paris Saint-Germain and Liverpool.
Having sat out those two matches already, the France striker was free to play and after helping to get the result he echoed the sentiments of Kolasinac when it came to making more of an impact in the first leg.
So we have been paired with Napoli for the quarter-finals of the Europa League, and it is probably the toughest opponent we could have got other than Chelsea.
United have a Premier League meeting with West Ham at Old Trafford in between those two games, with away trips to Wolves and Everton coming either side of them.
"Having said that, Arsenal are a great team and it'll be a very hard task for Napoli to get past them into the next round".