The Blues are expected to be busy over the coming days due to the need to ensure that they meet the Premier League's Profit and Sustainability regulations.
Co-owners Todd Boehly and Clearlake Capital have always maintained that they will comply with such rules, yet work is clearly being undertaken with Ian Maatsen said to be on the way to Aston Villa and Omari Kellyman surprisingly moving in the opposite direction.
As a result, there could be more movement in and out of Stamford Bridge before June 30, the final day for the latest accounts, but Forest also find themselves in a position where they must raise funds themselves.
Reports have indicated that one major sale could be enough to fulfil the relevant criteria and, according to John Percy of The Telegraph, that could be achieved through the sales of Moussa Niakhate and Orel Mangala.
Nevertheless, the same report is alleging that Chelsea are making an attempt to convince Forest to cash in on star man Murillo.
How much may Murillo cost?
Forest are said to want in the region of £70m if they are to agree to part ways with a player who they only signed for approximately £12.5m last year.
Such was the impact of the 21-year-old that he went on to make 35 starts in his debut season in English football, leading to him being named as the club's player of the season.
With a contract in place until 2028, Forest ideally do not want to part ways with the former Corinthians man ahead of next season.
Nevertheless, there will be an understanding that they can significantly benefit from a sale involving anywhere close to the numbers that they would ideally like to generate.
How will Chelsea react?
Chelsea reportedly view Murillo as someone who is of the ideal profile for their side, with the player regarded as having high potential.
Boehly and Clearlake Capital have also been relentless in signing young Brazilian players, albeit directly from their homeland rather than before they have arrived in England or gone elsewhere.
That said, a fee of £70m will almost certainly be beyond Chelsea at this point in time. There have been reports that they were not prepared to meet the wage demands of the likes of Michael Olise and Nico Williams, and similar may apply here.
From Murillo's perspective, he will be aware that he has admirers at more than just Chelsea, which may plausibly lead to him biding his time before making any decisions on his next move.