The Colombia star spent the previous two seasons on loan at Bayern Munich, who opted not to exercise its option to make James's deal permanent.
It has left him in a state of flux with LaLiga giant 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.
Napoli is reportedly the frontrunner to capture the attacking midfielder's signature and it is a move that would see James once again join up with Ancelotti, who took him to Madrid and Bayern.
Atletico Madrid has also been linked with a move to prise him from its rival but James, speaking to reporters after Colombia was 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 has won two UEFA Champions League winners' medals and a LaLiga title with Madrid, while he also collected a pair of Bundesliga trophies and a DFB-Pokal with Bayern.