According to reports, City are plotting a £75million offer for the 22-year-old at the end of the season but Chelsea are also said to be ready to counter the bid.
Anderson has been impressive for Forest since joining from Newcastle United in 2024, featuring in 51 matches in all competitions, scoring twice and providing seven assists.
The Englishman has played every minute in the Premier League and Europa League this season under former manager Nuno Espirito Santo and his successor Ange Postecoglou.
Despite Forest's bad start to the season which sees the team lying in 17th position on the Premier League table, Anderson has started the last four matches for England under head coach Thomas Tuchel.
The former Scotland youth international has managed only been substituted once for England, helping the team to four consecutive victories without conceding a goal.
Ironically, the midfielder is set to return to Premier League action when the Reds host his admirers Chelsea at the City Ground on Saturday.
Bradley Barcola is available for Liverpool's Premier League meeting with Brighton at Anfield on Sunday, but Dominik Szoboszlai has been ruled out as the Reds continue a demanding run of fixtures.
Arsenal manager Mikel Arteta could hand Max Dowman an increased role in the first team after Bukayo Saka was ruled out for up to eight weeks with a quad injury.
Manchester United head coach Michael Carrick will be looking for an immediate response when his side host Bournemouth at Old Trafford, after their humiliating Champions League defeat to Como.
Oliver Glasner has praised Nottingham Forest's determination after they were held to a 1-1 draw by Ipswich Town, insisting his team had created enough chances to take all three points.
