The Merseyside clubs are among those interested in the 22-year-old marksman.
The 22-year-old has emerged as one Dutch football's brightest prospects after netting 21 goals in 28 starts for the Eredivisie giants this past season.
Liverpool are expected to shift Mario Balotelli and Christian Benteke off their books in the summer, meaning there could be space for another frontman to come in, while the Toffees have to accept the possibility that red-hot striker Romelu Lukaku may be prised away.
Both Premier League sides are interested in Milik but, according to Estadio Deportivo, they could struggle given the huge competition, also reporting interest from Arsenal, Barcelona, Inter Milan, Juventus and, significantly, Sevilla.
The newspaper has quoted Milik as saying that he would favour a move to Sevilla, noting that his preference is the Spanish top flight.
He said: "Sevilla is a great club playing in a great competition. I do not hide that the Spanish League is my favorite option."
The report cites €15 million (£10m) as a potential figure, but his reported suitors would do well to snap him up before Euro 2016 incase Milik's value increases as a result of a goal-laden campaign with Poland.