The 30-year-old is impressing at the 2022 World Cup, scoring two goals and providing one assist in two games for his country.
He already made his mark this season at the club level for FC Porto, finding the net 13 times and setting up eight assists in just 19 matches.
Taremi was purchased from Rio Ave in the summer of 2020 for €4.73m, but his value on the transfer market has quadrupled to at least €20m.
Lazio had been adamant it did not need to bring in another striker, despite suffering in the absence of injured Immobile, football-italia.net reported.
The team could only really consider signing a new player if he could provide versatility, to be both the understudy to Immobile and his potential strike partner.