The 18-year-old wide attacker is widely hailed as one of the best teenagers in English football, and has been a Cottagers first-team player since the latter stages of the 2013/14 campaign.
Roberts, an England U-19 international, is believed to have emerged as a target for the Citizens of late, and now reports claim that a £5m up front fee has been settled with the West London side, although this figure could rise to £10m with add-ons.
Fulham had planned to keep the youngster, but with his contract set to expire in a year’s time, the lure of guaranteed cash from City appears to have swayed their stance.
The move for Roberts could be a response to home grown player issues at the Etihad Stadium, with exits of James Milner, Dedryck Boyata and Micah Richards having depleted the club’s already slim numbers.
The Fulham ace made his Premier League debut in 2014 and featured 20 times from the Craven Cottage outfit in the Championship last term.