Media playback is not supported on this device
West Ham manager Slaven Bilic questioned Dean's decision to send off Sofiane Feghouli in his side's 2-0 defeat by Manchester United on Monday.
It was the fifth red card Dean has shown in 15 matches this season.
The Hammers are appealing against Feghouli's dismissal.
Dean sent off the Algeria international midfielder after just 15 minutes following his collision with Phil Jones, but Bilic felt the United defender had committed the more dangerous tackle.
The dismissal was the 25th by Dean since the start of the 2013-14 season - the highest number by any current Premier League referee in that period.
Writing in The Times, former player Tony Cascarino said Dean "lost all control of the game" while Sky Sports pundit Niall Quinn called Dean "arrogant" and the decision "rank bad refereeing".
But former Manchester United captain Gary Neville later tweeted: "I was critical of Mike Dean's performance in the game. He was poor. But I think the reaction since towards him is disgraceful.
"Yes, he should be criticised but to suggest he wanted to be centre of attention and he should be sacked or not referee again is wrong!"
Sunday's FA Cup match between Tottenham and Aston Villa is live on BBC One from 15:35 GMT, and full match commentary will be available on BBC Radio 5 live from 16:00 GMT.
Mike Dean will referee Sunday's televised FA Cup third-round tie between Tottenham and Aston Villa - despite recent criticism of his performances.