According to BBC Sport, the Toffees are negotiating a £12 million deal to bring the 27-year-old to Goodison Park.
They were linked with the forward last summer but a move didn’t materialise due to the Saints’ excessive demands.
The Merseyside club signed Neal Maupay from Brighton & Hove Albion, but he scored just once in 27 Premier League appearances last season.
Everton have revived their interest in Adams to bolster their attack, but they face competition from Crystal Palace who are also keen.
The Scotland international isn’t a prolific goalscorer but is viewed as an effective all-round player who is suitable to play the lone striker role.
The 27-year-old moved to Southampton in 2019 after impressing with his displays at Birmingham City.
He made a slow start to life in Hampshire but has since established himself as a key member of the first team.
Adams has made 125 Premier League appearances for Southampton, registering 27 goals.
He netted five goals in 28 top-flight appearances last season as the Saints suffered relegation to the Championship.
The forward has now made a flying start this term, scoring goals in their opening two matches against Sheffield Wednesday and Norwich City.
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