United's interest in the Brazil international is not new. They followed him extensively last season and explored the possibility of a deal, at a time when Forest's position was more vulnerable. A valuation of around £60-70 million was touted if the club were relegated.
Forest ultimately stayed up - and Murillo's position has strengthened since then.
He signed a new contract in May and Forest are under no pressure to sell. That means the figures previously discussed are no longer a useful guide to what it would take to prise him away.
A huge offer would be required, and January is not a time when United would expect to land him.
Sources say United’s interest is more relevant to their longer-term planning, especially with further decisions coming in defence.
As we have reported, United continue to admire Jarrad Branthwaite, while other centre-backs are also being assessed as they look at how the position could evolve. Murillo belongs in that conversation.
His age, Premier League experience and ability to defend aggressively while remaining comfortable in possession make him the type of centre-back United can see fitting into their long-term plans.
He would also represent a significant investment, which is why his situation is more likely to become relevant when the club are prepared to make a major defensive commitment.
He has an opportunity to strengthen his Premier League credentials in the coming weeks, with Forest facing high-profile tests against Arsenal and Manchester City before the next international break.
Those games will provide Murillo with another chance to measure himself against two of the division’s best teams.
Liverpool and Chelsea may be the clubs generating the most Murillo speculation at present, but United’s interest should not be dismissed.
They have certainly been monitoring him and remain ambitious about the possibility of signing him if it becomes possible