Fresh claims from Italy suggest the race for the Colombian is continuing to grow.
Ríos has been one of the busiest names in the transfer rumour mill in recent weeks. Manchester United, Fulham and, more recently, Bournemouth have all been credited with interest in the midfielder.
Napoli have consistently been described as the Italian club pushing hardest for his signature.
According to Italian journalist Salvatore Ferrante, Everton have now joined Bournemouth and Fulham in showing interest in Ríos.
Fulham's name has appeared regularly across reports from Colombia, Portugal and Italy, while Bournemouth only emerged as a potential suitor last week.
Everton, though, are a completely new addition to the picture.
Their interest further strengthens the impression that Premier League clubs continue to monitor the Colombian closely.
Even so, there remains little evidence that any English club has progressed beyond the enquiry stage.
Napoli continue to be viewed as leading the race for Ríos.
Ferrante's report also contains a new detail, claiming that if Ríos does leave Benfica, his preferred destination would be Napoli because of the opportunity to play Champions League football.