Everton have not ruled out a deal to bring Wayne Rooney back to Goodison Park, Sky sources understand.
The 31-year-old is likely to leave Manchester United this summer, having found opportunities limited under Jose Mourinho last season.
The United captain, who left Everton for Old Trafford in 2004 as an 18-year-old, has previously said the Toffees remain one of only two Premier League clubs he would play for.
Sky Sports News HQ also understands Everton have identified Arsenal forward Olivier Giroud as a forward option, with Romelu Lukaku having said he has reached "an agreement" with another Premier League club.
Any deal for Giroud would be dependent on agreeing an appropriate price with Arsenal, while the Frenchman is also the subject of interest from West Ham, according to Sky sources.
Giroud scored 16 goals last season, but started only 11 Premier League matches with manager Arsene Wenger preferring to deploy Alexis Sanchez in a central striking role.
Arsenal could complete their own big-money signing for a striker "within the next day or two", Lyon president Jean-Michel Aulas has confirmed, with Alexandre Lacazette close to a club record £43.8m move.
Sources close to Giroud indicate he will wait to see what players Arsenal bring in this summer before making any decision regarding his future.