Since the departure of Carlo Ancelotti from Everton, Rodriguez's future at the club has been in the dark.
James has still not featured for Everton under new manager Rafael Benitez this season after joining the side for a nominal fee a year ago.
The Colombian midfielder has missed several games because of coronavirus-related issue, playing his last game for the club in a 1-0 defeat by Sheffield United on 16 May.
Everton would somehow be free from financial constraints should they sell James whose wages is reported to be £200,000 a week to another club.
Benitez after completing his move to Everton disclosed his frustration about his inability to sign more players due to Financial Fair Play rules, insisting the situation had "killed" the club.
Ahead of Everton's win over Burnley on 11 September, Benitez said of Rodriguez's future:
"It's always up to the player. In the end he has the final decision. Some markets are open and then we had some problem with the Financial Fair Play rules, so we need to consider any option and see what happens."
Rodriguez, a former player for Real Madrid who has also featured for Porto, Monaco and a loan spells with German Bundesliga giants Bayern Munich.
Everton are currently sixth in the league log with ten points after five games.
