The Brazil midfielder appears to have been frozen out by United manager Ruben Amorim.
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Local journalist Jorge Nicola is reporting that Flamengo are studying the possibility of agreeing a loan for Casemiro.
The transfer window closes in Brazil on February 28.
The midfielder was the subject of some rumours last month regarding a possible move to Roma, although it never materialised.
Casemiro is also on the shopping list of Saudi Pro League clubs.