Wood was asked about Anderson's situation in a Sky Sports interview after the friendly, with the two players having gone head-to-head in Tampa as England defeated New Zealand 1-0.
"It would be fantastic if he stays. He is still a Forest player, and we want to keep him.
"Time will tell what will happen. It is up to those with the power to make a decision."
Anderson has been one of the outstanding midfielders in the Premier League this season, his performances for Forest a primary reason the club avoided relegation and reached the Europa League semi-finals.
Manchester City's pursuit is well-documented — they have already had one bid rejected — with Nottingham Forest holding firm at approximately £100m, a figure calibrated against Arsenal's £105m purchase of Declan Rice in 2023.
The Athletic and BBC Sport have both confirmed that price point. City are expected to submit a second bid, and whether Anderson's World Cup form with England gives Forest additional justification to hold their valuation — or whether City eventually find a package that meets it — will be the defining transfer subplot of the summer once the tournament concludes.