The Uruguay international will be out of contract in the summer and interim boss Ralf Rangnick confirmed, as expected, that the striker is set to depart Old Trafford.
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However, Edi led the line at Selhurst Park, with Cristiano Ronaldo and Marcus Rashford among those who were ruled out of action.
“It would be good to finish this season with a good game, three points, and I’m pretty sure the team sees it the same way,” Rangnick revealed to MUTV before kick-off in south London.
“Out of our starting XI, there will be 10, apart from Edi Cavani, who will still be playing for this club next season.
“I presume they’d much rather play in the Europa League than the Conference League.”
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Crystal Palace grabbed a slender victory against United while West Ham United lost at Brighton & Hove Albion, the Reds in that way qualified for the next season’s UEFA Europa League.
Cavani made his 59th appearance for the club, against the Eagles, and scored 19 goals, 12 of them in the top flight.
It remains to be seen where his next destination is going to be.