It has left James in a state of flux with La Liga giants Madrid seemingly keen to cash in having spent heavily to bring Eden Hazard and Luka Jovic to the Santiago Bernabeu to reinforce Zinedine Zidane's squad.
Atletico Madrid have also been linked with a move to prise him from their rivals but James, speaking to reporters after Colombia were eliminated at the Copa America by Chile, is in no immediate rush to decide his next move.
"I don't know yet where I will play next season," he said. "I have another three weeks to think about it.
"It doesn't just depend on me, [I] have to see what Real Madrid will decide. There are people inside who decide a lot, I can't do anything."
James' father has suggested that a move to Italy would be the preferred choice for his 27-year-old son this summer.
“I think a new change is what he needs for his career now, and [fellow Colombian] David Ospina is at Napoli now and I think he is very important,” Wilson Rodriguez told CalcioNapoli.
“Napoli are the best option for him.
“He has character and personality. Even at times of adversity, he’s always come out strongly. He was born for this, thank God.
“Between him and Ancelotti, there was immediately a lot of respect. James is grateful to Carlo for what he did, he knows how to get the best out of him and that contributed to their great friendship.
“The coach has always been very happy with his performances. I’ve heard about [the speculation] and I think a change is what he needs right now.”