The Sun says both Manchester giants are going head-to-head for the Geordie.
And with the World Cup looming this summer, the plan for United and City is to close the signing of Anderson before the summer window opens on June 15.
With England's World Cup campaign kicking off on June 17 against Croatia, Anderson could be turn out for the Three Lions with a new club next to his name.
Anderson is rated at £100m by Forest with United believing they have a genuine chance of trumping City for the midfielder thanks to the team's resurgence under manager Michael Carrick.
In contrast, City could be in flux, with Pep Guardiola refusing to commit to next season and insisting no decision will be made until the summer.
