Manchester City writes on its website that Anderson, 23, has undergone a medical in Kansas and that the clubs have now agreed on the deal.
The final details will be worked out when he returns to England after the World Cup.
Manchester City's previous transfer record was £100m, which the club paid for Jack Grealish when he joined from Aston Villa five years ago. According to Sky Sports, Anderson will become the most expensive British player to date.
The Athletic writes that Nottingham is expected to use part of the transfer fee to try to sign Lucas Bergvall from Tottenham.
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