The two biggest clubs in Spain are both expected to sign a new centre-back in the summer of 2025, and there have recently been claims that Murillo has emerged as a target for the duo.
The 22-year-old arrived at Forest from Corinthians in August 2023, with the Premier League club believed to have paid in the region of £10.6m for his signature.
Murillo was excellent during his first season in English football, making 36 appearances in all competitions, while he has also had a strong start to the 2024-25 campaign.
The South American has another four years left to run on his contract with Forest, and the Reds are said to be determined to keep hold of him amid the ongoing transfer speculation.
Forest want 'huge fee' for Murillo amid Real Madrid, Barcelona talk
However, according to Football Insider, Forest would accept a 'huge fee' for him, with the club accepting that it will be difficult to prevent the defender from leaving in the near future.
The report claims that Forest would want a 'huge profit' on Murillo, and a number of Premier League clubs are said to be keeping a close eye on his situation with a view to a potential move.
Murillo only made 27 appearances for Corinthians before moving to English football, and he is yet to make his debut for Brazil despite his excellent performances in the Premier League.
The Telegraph reported earlier this year that Forest value Murillo at £70m due to his strong form, but it is highly unlikely that either Barcelona or Real Madrid would prepared to go to that fee.
Real Madrid's centre-back need is more pressing
When Barcelona have a fully-fit squad, there are a number of centre-back options available to head coach Hansi Flick, with Pau Cubarsi, Ronald Araujo, Andreas Christensen, Eric Garcia, Jules Kounde and Inigo Martinez all at the club.
However, the same cannot be said for Real Madrid, as the Spanish and European champions decided against replacing Nacho last summer when the Spaniard decided to leave on a free transfer.
Jesus Vallejo is allegedly not in the club's plans, with the defender set to leave next year, while there are concerns over David Alaba's long-term fitness, with the Austrian out since last December due to a serious knee injury.
A new centre-back is believed to be a priority for Los Blancos next summer, but it is difficult to imagine Murillo arriving at Bernabeu if Forest, as reported, want as much as £70m for his signature.