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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.

As a teenager he tried three times, unsuccessfully, to defect from Cuba, once spending a month in Cuban jail. He finally escaped to Mexico on his fourth attempt, saving his mother from drowning on their boat trip over.
He and his mother were then reunited with his father in Tampa, Florida where he had fled two years earlier.
But Fernandez's transition from his life in Cuba was difficult. Baseball helped him acclimate to his new American life.
After starting at Alonso High School in Tampa, speaking almost no English, Fernandez steered the baseball team to two state championships.
He was drafted by the Marlins in 2011 at 20 years old and named National League Rookie of the Year in 2013.
The Miami Herald reported his grandmother, a loyal supporter, often stood on her roof in Cuba during his games to listen to the sports radio broadcast as her grandson played.
Players and fans described him as enthusiastic, energetic and charismatic. Many Cubans from Miami's Latin community, felt that the player embodied their own struggles.
Miguel Garay, 78, a Miamian who came from Cuba's Pinar del Rio said: "His story was our story.
"There's such a great tradition of baseball in Cuba and he embodied it better than anyone."
After undergoing surgery in 2014 for a torn elbow ligament Fernandez became a US citizen in 2015, where he gave the keynote speech at his citizenship ceremony.
He said: "This is one of my important accomplishments. I'm an American citizen now - I'm one of them. I consider myself now to be free."
Fernandez was described as an "avid fisherman" and was aboard a friend's boat when the vessel hit a jetty, causing it to capsize.
He had revealed recently that his girlfriend was pregnant.
Marlins President David Samson said at a news conference: "When you talk about tragedy like this there are no words that come to mind.
"There is prayer and thought toward his family and his soon to be born daughter. You recognize how precious life is."
Mike Dean will referee Sunday's televised FA Cup third-round tie between Tottenham and Aston Villa - despite recent criticism of his performances.
[NEXT_CONCEPT]
Jose Fernandez, the talented 24-year-old baseball star who died in a boat crash on Sunday, was heralded by baseball commissioner Rob Manfred as one of the game's "great young stars".