The 23-year-old has not featured in either of Everton's two Premier League games this season.
Sevilla are interested in securing the Scotland international on a season-long loan.
Patterson, who made just 10 league appearances for Everton last term, is likely to find regular first-team opportunities in La Liga.
Sevilla's current right-back, Juanlu Sánchez, is in negotiations to join Serie A champions Napoli, with Patterson seen as his replacement.
The former Rangers player, who joined Everton in January 2022 in a £16 million deal, has struggled for game time.
He did not feature in the recent match against Brighton, which Everton won 2-0, marking their first game at the new Hill Dickinson Stadium.
However, a deal with Sevilla is still a fair way off from being finalised.