The 20-year-old forward has appeared as a key transfer target for the two Championship clubs this summer.
Middlesbrough boss Neil Warnock wants to add more goals to his squad ahead of the new season and the club held lengthy discussions on Monday over signing Muniz.
Fulham are also interested in the forward and want to sign him as they look to bounce straight back up to the Premier League next season.
Flamengo are aware of the interest Muniz has been attracting and according to Brazilian outlet UOL, they have scheduled a fresh meeting in Lisbon to discuss the striker’s departure.
The forward’s agent will be part of the summit today as they look to find a solution for the young forward’s future.
Middlesbrough are looking to sign Muniz on loan with an option, or potentially an obligation, to buy.
Apart from the Championship, Muniz has also been attracting the interest of Saudi Arabian outfit Al Nasr this summer.
They are willing to offer €4m to secure 50 per cent of the striker’s economic rights.
It is claimed that today’s meeting could be decisive and a decision could come within the coming hours.