The Toffees were linked to the capture of Diaz over the summer, with a potential swap deal tabled that would have seen his compatriot James Rodriguez return to Porto in exchange.
Talks eventually broke down between the clubs, seeing the Colombian remain with the Dragoes heading into the new season, and he has kicked off the campaign with four goals in five Primeira Liga appearances so far.
According to Marca, Porto have reassessed their valuation of the 24-year-old since the beginning of the season, and could now demand a fee out of the Toffees' budget, should Rafael Benitez opt to stage another attempt to secure his signature in the January transfer window.
With Barcelona also recently enquiring, the Merseyside outfit now face intense competition, and could be forced to search elsewhere if they are unable to meet Sergio Conceicao's demands.