Jesus is currently under a contract that pays him around £65,000 a week, and according to Daily Mail, his representatives were unimpressed by the club's offer of £90,000 until 2023.
The 20-year-old's current deal runs until 2022, so there is no rush, and there are no fears of him going elsewhere this summer.
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City decided to reward the Brazil international with a new and improved deal after his brilliant start to life in the Premier League and a compromise seems imminent.
The goal-scoring machine just confirmed his value, netting the winner in Brazil's 1-0 victory over Germany on Tuesday.