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The Brazilian's new deal would see him earn£150,000 a week and he is currently contracted at the Etihaduntil 2023.
The David Beckham-owned club are keen to sign more big-name players after a disappointing first MLS season.
“Everton were really struggling for money at the time and I found out they were listening to offers from people as well. They were trying to push me to sign for Chelsea because they were going to pay the most money," Rooney told the UTD Podcast.
"But, once I knew United were interested, I wanted some confirmation that they did want to sign me. Once I knew they did want to sign me, it was the only club."
The shot-stopper wants to be No.1
Manchester City will shift their attention to locking down Raheem Sterling after Pep Guardiola committed to the club.
The Mirror claims the club's new priority is ensuring both Sterling and Kevin De Bruyne also sign contract extensions.
The duo are expected to be offered improved deals worth around £350,000 a week.