Diaz was heavily linked with a move away from Porto last summer and Everton tried to do a deal to land the player for James Rodriguez on loan and a cash sum.
But the deal did not come to fruition and Diaz continued at Porto, where he has scored seven goals in eleven appearances across all competitions this season.
Several clubs are again believed to be interested in signing him ahead of the winter window and the player wants to move to the Premier League.
And according to Portuguese daily Correio da Manha, Porto are considering whether to let the player go in January and bring in cash for their coffers.
The Portuguese giants are torn over whether to hold on to him until the summer or bring in the funds by selling him in January.
If Porto reach the last 16 of the Champions League, the club are likely to favour keeping him until the summer.
But there is a real possibility that the Portuguese giants will cash in on him in the winter transfer window.
He has an €80m buy-out clause in his contract but Porto are expected to negotiate if they receive a fee in the region of €60m in January.