Toffees boss Rafael Benitez has managed Rondon twice previously and wants the striker at Goodison Park before the transfer window closes.
The 31-year-old is on the books at Chinese side Dalian Professional and Everton are continuing to work on a deal to sign him.
Rondon has turned out in England for West Brom and Newcastle United, making just ten appearances shy of 150 in the Premier League.
While Everton are in for Rondon, they have not bid for Manchester United winger James.
The Wales international is travelling to Leeds this evening as he moves to complete a switch to Leeds United.
It had been suggested Everton could also move for the winger.
However, they have not done so and Leeds are to pay a club-record fee of £25m plus £5m in add-ons for James.
