Sources close to Santiago Bernabeu have confirmed to Goal that Real want James sold as quickly as possible, ideally within the next 10 days.
Indeed, Madrid players that are not on extended breaks are due to report back on July 8, although James's involvement with Colombia at Copa America means he was not required to return on that date.
That gives the Liga club, who are not interested in sanctioning a further loan deal, more time to negotiate James's exit, with Serie A side Napoli the front-runners to sign the midfielder for a fee expected to be in the region of €30 million to €40m (£36m/$45m).
Aurelio De Laurentiis, Napoli's president, confirmed the club's interest in the Colombian back in June, insisting that he had been requested by manager Carlo Ancelotti, who originally signed him for Madrid from Monaco in 2014 and also took him to Bayern Munich.
"James Rodriguez is Ancelotti’s wish," De Laurentiis told Radio Kiss Kiss in June. "I don’t know if we need him 100 per cent, but his talent isn’t in doubt.
"I must help my coach. He wants James and I won’t bat an eyelid, even if he’s very expensive."
Despite arriving at Madrid with considerable fanfare after his exploits in winning the Golden Boot at World Cup 2014, James failed to make a significant impact in the Spanish capital and was loaned out to Bayern in 2017.
His two-year loan has now come to an end, however, with the Bundesliga champions deciding against taking up their €42m (£38m/$47m) option to sign him on a permanent deal.
Ancelotti's Napoli are confident of getting a deal over the line before the end of the month, with the first-team's pre-season return date set for July 6, when they will head to Trentino for 20 days for the first part of their preparations.
Madrid, for their part, are looking at offloading a number of first-team players before they head to the United States for the International Champions Cup.
Isco and Gareth Bale are two more Madrid want to offload although the latter's huge wages, along with his determination to stay at the club, mean it remains a difficult process in getting him out.
In terms of incomings, meanwhile, Zinedine Zidane's side have cooled their interest in Neymar with a view to securing a future move for Kylian Mbappe, while Paul Pogba remains a top target for this summer.