The 22-year-old has emerged as a target for both Real Madrid and Barcelona after showcasing his defensive qualities during his time at the City Ground.
Murillo, who completed a move from Corinthians in August 2023, quickly established himself as a regular fixture in the Forest side, starting 32 Premier League matches during his first season in the English top flight.
The centre-back has remained a prominent figure in the backline for the current campaign, having started all 11 of Forest's Premier League matches this season.
Murillo has played his part in a Forest defence that has conceded just 10 goals in 11 league matches, leaving the Reds with the second-best defensive record in the top flight.
Real Madrid told to double Murillo valuation
Having been left impressed by Murillo's performances, Real Madrid are believed to be eyeing a potential January move for the Brazilian.
However, according to the Daily Mail, Los Blancos will have to double their £40m valuation if they are to have any hope of signing Murillo in the new year.
If Forest were to consider offers in the £80m range, it would represent a significant mark-up on the reported £10.6m they paid Corinthians to sign him in 2023.
The report claims that Forest are reluctant to sell any of their key players in the middle of the season, especially as they are sitting in fifth place and looking to mount a bid to secure European qualification.
Forest are under no immediate pressure to sell Murillo, with the defender under contract until the summer of 2028.
Why are Real Madrid targeting Murillo?
Los Blancos are weighing up whether to strengthen their backline in January after being left short in central defence following Eder Militao's season-ending injury.
Militao recently suffered an anterior cruciate ligament injury for the second season in a row, adding to Carlo Ancelotti's injury woes.
The Real Madrid boss is already without the services of David Alaba, who is struggling to work his way back from his own ACL injury.
Aurelien Tchouameni can provide cover at centre-back, but the Frenchman is currently sidelined with an ankle problem.
As a result, Ancelotti is left with Antonio Rudiger and Raul Asencio as his two main central defensive options.
The Real Madrid boss can also call upon Jesus Vallejo, but he does not seem to have much intention of utilising the 27-year-old despite having little cover in central defense.
Real Madrid will look to find solutions within their squad until the new year when they can look at the possibility at strengthening their backline.