The former Brazil international - who also revealed he’s in talks over a return to Madrid - says he could take his compatriot from Barcelona to the Spanish capital.
Still just 23, Neymar finished third in Monday's Ballon d'Or and has an integral figure in the Barca side since his big-money switch from Santos in 2013.
However Carlos - who made over 500 appearances across an 11-year spell with Madrid - suggests he could facilitate a transfer in the future.
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"I can bring Neymar to Real Madrid," the 42-year-old said in an interview on Punto Pelota.
"He is still very young and I am sure next year he will finish even higher in the Ballon d'Or."
Carlos also spoke about a return to the club in a coaching capacity to assist former team-mate and new Madrid coach Zinedine Zidane.
"I had a meeting with Real Madrid about my future with the club," the 42-year-old added.
"It would be an honour to work with the club, we should know how [we will] collaborate [with Zidane's Madrid] on Friday."