Martinez was blanked by manager Michael Carrick after conceding a penalty and receiving two yellow cards in the space of 82 seconds during the defeat against Chelsea over the weekend.
Asked afterwards if he felt let down by Martinez, Carrick said he had not had a chance to view the incident again.
"I've not seen it back, so I don't know if it was or not. It's a big moment in the game. The second goal and losing a man at that stage had a big influence on it, for sure."
The World Cup winner was already under scrutiny following his public criticism of United’s hierarchy earlier in October and now his poor defending and lack of discipline have led to questions being asked about his future.
As per the Manchester Evening News, the Red Devils will host a meeting this week to speak on his current deal, which expires in 2027, his poor form and transfer interest from Atlético Madrid, Barcelona and several Italian clubs.
United risk losing Martinez for free when his contract expires next year and the side may be seeking a January switch for the defender, who is a liability at the back under Carrick.
A move away may be the best option for both parties and as the January window approaches, United may be seeking to bring in a fresh face at the back to help back away from relegation.