According to Ian Ladyman of the Daily Mail, Toffees boss Marco Silva wants to add more creativity to his side. Consequently, the club is ready to give the 31-year-old, who is a free agent, an opportunity.
As Ladyman noted, Nasri has been serving a ban from football as a result of an illegal treatment he underwent in 2016.
"The treatment, taken while on holiday, was for hydration but was found to contain micronutrient components that were on the World Anti-Doping Agency banned list," Ladyman said. "Nasri was initially banned for six months, but that was subsequently increased to 18 months."
However, according to David Prentice of the Liverpool Echo, the Toffees aren't interested in snapping up the former Marseille star.
The Frenchman's last club was Antalyaspor in Turkey, although he only turned out for the team eight times, scoring two goals.
Prior to that, Nasri enjoyed a season on loan with Sevilla. In 2016-17, he made 30 appearances for the Andalusian club in all competitions and scored three goals. However, he excelled in a number of different roles for Jorge Sampaoli's team and showed he still had the class to make an impression at the highest level.
Per WhoScored.com, during his time with Sevilla he operated a little deeper and provided a controlling presence in midfield:
The worry for any club looking at him, in addition to the ban, would be the fact that he's not played in a top-five European league since his loan at Sevilla from City came to an end.
Everton have other options to call upon in this area of the pitch. While a quartet of Gylfi Sigurdsson, Richarlison, Bernard and Theo Walcott looks likely to be Silva's preferred attacking setup, in Ademola Lookman and Kieran Dowell the team have two bright, young creative players in reserve.
Lookman has yet to start a Premier League game for Everton this season but showed what he is capable of for England's under-21s in their 7-0 rout of the Andorra under-21s on Thursday:
Additionally, summer loan signing Andre Gomes and James McCarthy, who has been on the sidelines with a broken leg, appear to be close to full fitness too:
Nasri has experience in the Premier League, having enjoyed prosperous stints at Arsenal and especially City. At the Etihad Stadium, he won the title twice and was a key creative force for the team.
At Everton, he would offer another option in the final third or midfield for Silva, potentially making him a useful asset from the bench or in cup matches. However, given the array of young talent on the club's books, it would be a shame if a veteran arrived to hinder their progress.