It's understood that Atletico could land the 28-year-old if they're willing to dish out the €42 million that Real Madrid asked Bayern Munich to pay to make his stay permanent.
Rodriguez spent the last two seasons on loan in Bavaria but saw his spell with the Bundesliga side come to an end after Bayern declined to trigger a clause in the loan agreement.
A return to Real Madrid appears to be out of the question, as Rodriguez apparently does not figure into manager Zinedine Zidane's plans for the upcoming season.
Napoli have also been in negotiations to sign the Colombian but are struggling to meet Real Madrid's transfer demands, Corrigan adds.
Rodriguez's possible move across town would mark the second deal that the rivals have made this summer following Marcos Llorente's €40-million move to the Wanda Metropolitano.
Along with Llorente, Atletico also completed a lucrative deal to sign Joao Felix, 19, from Benfica for a club-record €126-million fee - the fifth-highest sum ever paid in football and the second-highest for a teenager.