The 31-year-old midfielder is a free agent after leaving Turkish club Antalyaspor in January and keen to return to the league where he enjoyed his greatest success.
The Frenchman is allowed to train with clubs again from next month when his drugs ban expires. Nasri is serving a ban after receiving an intravenous treatment from a clinic in Los Angeles in December 2016 when he was playing for Sevilla on loan from City.
The treatment, taken while on holiday, was for hydration but unfortunately, it was found to contain micronutrient components that were on the World Anti-Doping Agency banned list.
Initially, Nasri received a six-month ban, but later it was increased to 18 months after his appeal’s dismissal.
It is understood that Everton manager Marco Silva has discussed the possibility of bringing the former French international back to England with his staff.
If Everton do go ahead and sign the player, it’ll likely mean that Kieran Dowell is not ready for the senior squad quite yet and could go out on loan this January.