According to Daily Mirror, Southampton, Cardiff and Crystal Palace are keen on signing the 32-year-old.
However, it is Everton who should do everything to sign the former Premier League winner.
The Toffees are in desperate need of a number nine like Dzeko. The likes of Tosun has struggled to adapt to English football and Dzeko would be a massive improvement.
The Bosnian knows the Premier League well and his playing style suits English football too.
The 32-year-old could make a huge difference for Marco Silva’s side and given his age, he is likely to come for cheap as well.
It could be a masterstroke if Silva manages to pull off the transfer.
Dzeko has scored 63 goals in his last two seasons with Roma and he could take Everton to the next level. His hold up play, movement and finishing ability makes him the ideal partner for the likes of Richarlison and Walcott.