The Colombia international fell out of favour at Goodison Park after Rafael Benitez was brought in to replace Carlo Ancelotti in the summer.
Everton tried using James in a swap deal for FC Porto forward Luis Diaz, though they could not get the deal across the line.
Turkish outfit Istanbul Basaksehir also showed interest in James, but the 30-year-old ended up staying at Everton beyond the summer transfer window.
It then emerged on Monday morning that the former Real Madrid midfielder has travelled to Qatar to hold talks with an unnamed club.
The club in question has been identified as Al-Rayyan, who are managed by former Paris Saint-Germain boss Laurent Blanc.
Everton are optimistic that a deal can be agreed for James to join Al-Rayyan, but are likely to have to pay some of his wages.
While the Toffees could have to continue paying some of James’ wages, they will be keen to offload their highest-earning player.