City's opening offer of around 80 million pounds for the 23-year-old was rejected late on Wednesday night, but negotiations between the two clubs remain active, and there is growing belief a deal can still be reached.
Anderson has already given the green light to a move to the Etihad Stadium and has agreed personal terms as part of City's summer plans. His position has not changed, and he remains fully committed to joining City if an agreement can be struck.
The midfielder is understood to be pushing for clarity as soon as possible, ideally before England's opening Group L fixture against Croatia on June 17, so he can focus fully on Thomas Tuchel's World Cup squad without transfer speculation.
However, Nottingham Forest are standing firm. The club value Anderson at more than 100 million pounds and believe any fee must surpass the 105 million pounds Arsenal paid West Ham for Declan Rice. Such a figure would also break Manchester City's own transfer record of 100 million pounds for Jack Grealish.
Forest regard Anderson as one of the Premier League's standout young midfielders and a key part of their long-term plans, meaning they are in no rush to sell despite ongoing talks.
Behind the scenes, discussions are said to be continuing over a structure that could satisfy both clubs, with optimism that progress can be made within the next week. While City's first approach was turned down, there is no sense of negotiations breaking down.
City's sporting director Hugo Viana is a strong admirer of Anderson, viewing him as a potential cornerstone of the club's next generation due to his technical ability, athleticism and versatility.