Rodriguez wants to quit Real Madrid after struggling for a place in Zinedine Zidane’s side.
He has been linked with both Chelsea and Manchester United.
Express Sport understands Jose Mourinho could be set to swoop for the Madrid star in a bid to beat Antonio Conte to another signing.
And Diario Gol claim Rodriguez does NOT want to travel to America with the Real squad for pre season and wants his future resolved.
It is said Rodriguez could go off like ‘a bomb’ in the Madrid dressing room if his wishes aren’t granted and would be a disrupting influence.
Florentino Perez is keen avoid that issue and wants him gone, but only for the right price.
Madrid paid around £65m for the Colombia star three years ago after the Brazil World Cup.
And he started well but has struggled on Zidane. Last term he made just 13 starts in La Liga, but managed to chip in with eight goals.
The 25-year-old still has a huge profile and would be a massive signing commercially for either United or Chelsea, with his South American pull particularly strong.
Manchester United have already departed for their tour in America, where they will meet up with Romelu Lukaku.
Lukaku underwent a medical in LA this morning and will be confirmed as a United player tomorrow.
He will become United’s second signing this summer after Victor Lindelof.
And Madrid hope Rodriguez could follow as they look to fund a world record move for Kylian Mbappe.