Manchester City and Chelsea are reportedly interested in signing Anderson, with the latter's manager reportedly making a personal request to bring him to the Etihad in 2026.
Anderson's potential transfer value is estimated to be around £75m, making him a significant target for both clubs.
Chelsea is also monitoring Anderson's progress, having previously watched him play for Forest.
Anderson joined Forest in a £35m deal, leaving Newcastle due to the Premier League's Profit & Sustainability rules, which require clubs to balance their finances.