The 20-year-old will be in Glasgow on Monday to complete a medical and sign another loan deal with Celtic.
Roberts spent 18 months with the Scottish champions before moving back to City at the end of last season.
Nice and Southampton were reportedly interested in his services, but Roberts turned them down in order to secure a move back to Celtic Park.
The England under-20 international scored 17 goals for Celtic and helped Rodgers' side to a domestic treble last term.