The Italian is enjoying another excellent campaign at club level, scoring 30 times in 33 appearances in all competitions, including 27 in 26 Serie A outings.
The 30-year-old currently leads the race for the European Golden Boot, while Lazio are in a strong position when it comes to his future as they have him on a contract until the summer of 2023.
According to the report, though, Everton boss Carlo Ancelotti is determined to bring Immobile to the Merseyside giants ahead of the 2020-21 campaign.
The report claims that Immobile is happy in Italy, but Ancelotti's presence at Goodison Park could convince the experienced forward to try his hand in the Premier League.
The former Juventus youngster has scored 116 goals in 167 appearances for Lazio in all competitions.