Everton have identified Deportivo La Coruna's Lucas Perez Martinez as the striker to provide support for Romelu Lukaku.
Director of football Steve Walsh is a long-time admirer of Lucas, 27, who scored 17 La Liga goals last season.
The Spaniard is likely to command a fee in the region of £15m.
Lukaku had been strongly linked with a return to former club Chelsea but the Belgian has decided to stay at Goodison Park for at least one more season.
Manager Ronald Koeman confirmed the 23-year-old told him on Friday he wished to stay, with the possibility Lukaku may sign a new contract.
Oumar Niasse, a £13.5m signing, has been told he has no Everton future despite only arriving in January.
Everton still hope to do a deal for Sunderland's unsettled central defender Lamine Kone, while Koeman also wants to sign a goalkeeper.
The possibility of England international Joe Hart arriving on loan from Manchester City is being complicated by the possible £7m cost of a potential season-long loan, with Hart on a reported £135,000 a week at Etihad Stadium and a loan fee also being involved.
Koeman is also keen on bringing in cover at right-back with Republic of Ireland defender Seamus Coleman currently injured - and he is considering returning to former club Southampton to sign Dutchman Cuco Martina.
Koeman signed the 26-year-old last summer when he was at Saints and Martina appears surplus to requirements after Koeman's successor Claude Puel brought in Frenchman Jeremy Pied.