Nasri is free to play football again in November, when his drug ban expires, and Everton feel he could offer good value as a free agent.
The Frenchman has previously impressed in England with both Manchester City and Arsenal.
And Everton are now said to be considering bringing Nasri to Goodison Park to bolster their attack.
Silva wants another creative option added to his squad, even though Everton are fairly well stocked in the forward areas.
Silva reportedly views Nasri as a player who could offer strong back-up to the likes of Bernard and Gylfi Sigurdsson.
Everton have begun the season in a rather inconsistent manner, and currently sit in 11th place in the Premier League table.