The rumblings of discontent stemmed from the French midfielder's display in the 1-1 derby result against Atletico Madrid on Sunday.
Tchouameni started the game alongside 39-year-old Luka Modric in the heart of Madrid's midfield.
But by the end of the game, it was Modric who made the bigger defensive impact than his younger midfield partner.
The Croatian, who departed the game with 15 minutes remaining, finished with four ball recoveries compared to Tchouameni's five.
Modric, who is 39, nearly won the ball as many times as Tchouameni did against Atleti
But the real concern was Tchouaeni's display when compared to that of Madrid teammate Federico Valverde.
Valverde, who is also a central midfielder but often given more freedom when it comes to attacking moves, began the derby against Atletico Madrid as somewhat of a right midfielder.
The report also claims Valverde made nine ball recoveries and 'was seen at times running past his teammate to halt counter-attacks.'
It led Diario AS to state 'there is a certain concern over the performances of Aurelien Tchouameni.'
However, Madrid boss Carlo Ancelotti appeared to have no such issues with the French star's form.
'For me, Tchouameni did well, he had presence', Ancelotti said.
Tchouameni has made 97 appearances across all competitions for Madrid since his £85million move from Monaco in 2022.
But Ancelotti will soon have a decision to make with Eduardo Camavinga now back in action.
The 21-year-old has since recovered and was on the bench for Madrid's dramatic 1-1 draw against Atletico on Sunday but did not get on the field.
Atleti manager Diego Simeone and captain Koke did their best to calm their fans down to avoid any further punishment.
But Simeone's side would have the last laugh as Angel Correa scored a 95th-minute equaliser to ensure the hosts nicked a point.