The Frenchman is on the brink of completing a £24 million move to Madrid, meaning Rodriguez is likely to fall even further down the pecking order should he stay at the Vicente Calderón Stadium.
The Uruguay international struggled to hold down a first-team place under Diego Simeone last season, and is now expected to be surplus to requirements at the club.
However, conflicting reports today suggest that even if Rodriguez does make a move away from the Spanish capital this summer, he will not join Sunderland.
Gus Poyet has been outspoken in recent weeks regarding his desire to add new faces to his side as soon as possible.
The Wearside club saw no fewer than 12 senior players leave at the end of last season, and at the moment the Uruguayan manager is being forced to prepare for the upcoming Premier League campaign with an extremely slim squad.
Earlier this week Poyet admitted the club were going through the motions to sign Rodriguez, but remained realistic that the deal was far from done. He said: “He wants to play football, he’s desperate to be playing week in, week out.
“It’s ongoing. It’s a possibility, but it’s no more than that."
In light of today's reports suggesting that Sunderland was no longer an option for Poyet's Uruguayan compatriot, it's unclear exactly where the 28-year-old's immediate future lies.
Rodriguez announced his intention to leave Madrid last week, and the signing of Griezmann makes it almost impossible for the midfielder to go back on his decision. But with no other reported interest from elsewhere, surely Sunderland has to be the destination.