Rafael Benitez wants to land the Colombia international winger, who shone at the Copa America in the summer.
Everton are closing in a deal which would see a fee of £21.5m paid to Porto and James go the other way on loan.
However, the deal is not done yet and talks have continued to take place over the weekend as the clock ticks down on the transfer window.
It is claimed that the involvement of James in the deal complicates matters.
Porto must agree terms with James if they are happy with the full package on offer, while the former Real Madrid man must also be happy to move to Portugal.
A positive for Everton is that Diaz would like to make the move to Goodison Park.
Everton are also exploring a deal to sign former Newcastle United attacker Salomon Rondon, who has twice played under Benitez.
