Palacios is set to showcase his talents when River take on Boca Juniors in Copa Libertadores final second leg on Sunday.
The monumental clash is set to take place at Real’s Bernabeu home after crowd violence forced the game out of South America.
Premier League giants Manchester United reportedly sent a scouting team to watch Palacios in action in the first leg which ended in a 2-2 draw.
But Renato Corsi, the creative midfielder’s agent, believes his client is most likely to end up playing for Los Blancos.
“We’ve received phone calls from Inter, Roma, Wolfsburg,” he told Spanish newspaper AS.
“A lot of clubs have shown an interest but the one who are really pushing hard for Palacios is Real Madrid.
“Due to the aftermath of the River–Boca return leg being postponed, presidents from both clubs haven’t been able to talk about the matter yet.
“Real Madrid have comported themselves really well with us, both with my and my partner.
“The two clubs will sit down to talk properly after the final, there will be a few meetings regarding Palacios in Madrid over the next few days.”
Real are reportedly seeking a successor to Ballon d’Or winner Luka Modric.
The Croatian star’s contract is up at the end of next season and Real see Palacios as the man to take up his role long term.
Corsi thinks the 20-year-old will use the Libertadores final as to prove himself worthy of the famous white shirt.
He added: “As a lifelong River fan and player who has spent a decade at the club, he wants the final to be played at the Monumental, in Argentina.
“But in light of the problems the other week, he’s happy to play the game at a great stadium like the Bernabéu and in such a beautiful country as Spain.
“Hopefully it will all go well for him and he will end up playing for Real Madrid”
Real Madrid play Melilla in the second leg of the round of 32 in the Copa Del Rey today (3.15pm).