The Colombian ace joined Everton on a free transfer from Real Madrid last summer, and was seen as a huge coup by the club after spells at the top of the game with both Madrid and Bayern Munich.
The 30-year-old linked back up with his ex-Real boss Carlo Ancelotti at Goodison Park but, after a quick start, his Premier League impact later dropped off.
New manager Rafael Benitez clearly has no interest in the playmaker, who is yet to feature this season, and tried to offload him to AC Milan, FC Porto and Istanbul Basaksehir in the summer transfer window.
James looked set to stay at Everton after all major European transfer windows closed, with Benitez admitting it was difficult to find a buyer Everton's highest earner, who is on a reported £200,000-a-week.
But it now understood he is in the Middle East in an attempt to move to the Qatar Stars League.
Rodriguez has flown out to the Middle East for talks with Qatari club Al-Rayyan, where he would link up with former France and PSG manager Laurent Blanc.
He would be the second big name to swap England for Qatar this summer after Toby Alderweireld's departure from Tottenham.
Earlier in the month, Toffees manager Benitez commented on the situation, saying: "It was not easy, because he was available in the transfer window. Now that we have just the Middle East window open, it's not easy."
James appeared to burn any remaining bridges with Everton last month when he revealed he didn't know who the team were playing in their next match.
On a Twitch gaming stream, James was asked if he would feature in Everton's next match and said: "I will start training on Monday, I think.
"On the weekend I will not play, I don't even know who Everton is playing, can you please tell me?
"I think it is away because the past was here at home," he explained, before someone gave him the answer.
"Ah, against Leeds they play, away from home, against Bielsa, a difficult game, let's see what happens, hopefully they win."
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