Forest hopes to build on a fantastic Premier League season in which they end in the seventh and secure a place in the Europa Conference League of next season.
According to ESPN, the side of Nuno Espirito Santo has now agreed a deal with Juventus in which Weah, 25 and Mbangula, 21, would go to the city.
The report adds that the reimbursement will be around € 22 million (£ 18.8 million/$ 25.6 million) for players with a combined 18 target contributions in 2024-25.
Weah is supposed to be enthusiastic because he hoped to book a place in the American team for next year's world cup on Home Turf.