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The English Premier League (EPL) heavyweights needed both Cavani and Greenwood at their best against Tottenham last weekend, where they came from behind to triumph 3-1 at the Tottenham Hotspur Stadium in London.
Greenwood came on as a second half substitute for Rashford and assisted Cavani's goal to make it 2-1, before scoring himself to make it 3-1.
Asked whether United should keep Cavani for another season, Neville told Sky Sports: "Tottenham had a throw with two minutes to go, and Cavani was moving between the centre-backs trying to stop the ball from being thrown in, and he's organising where Greenwood should be. I thought: 'Greenwood needs another year of Cavani being alongside him.'
"It inspired us as young players when you saw great players like Bryan Robson and Steve Bruce and Eric Cantona and Mark Hughes. And you see the best players in the world, or those who have been the best in the world like Cavani, doing his work like that in the 94th minute, someone like Mason Greenwood, who needs people who are mentors, good standards above him, who can coach him on the pitch, I just thought him and Marcus Rashford need another year of Cavani."
On the potential of Greenwood in the future, Neville added: "I know I speak a lot about Greenwood, but I do think he's a different level, with his composure and precision in the final third.
"I do think if Harry Kane gets injured, I look at that England centre-forward position and think: 'Who has his composure?'
"I do think Greenwood can play centre-forward in international football, it's whether he's got enough time to impress Gareth Southgate with a few weeks to go."
Manchester United play Granada on Thursday at Old Trafford, in the second leg quarter-final tie of the UEFA Europa League.
They hold a two-nil advantage against the Spaniards.