Monterrey coach Victor Vucetich has been suspended for two matches after insulting a referee and Guadalajara's Benjamin Galindo is in the eye of a storm after Saturday's 3-1 defeat at Cruz Azul.
Vucetich was banned "for one match for making constant claims or protesting the decisions of the match officials and another for a lack of respect towards them," the Mexican Football Federation said on their website on Monday night.
One of his players, Bernardo Hernandez, was also suspended for two matches for insulting the match officials during Monterrey's 3-1 loss away to UANL Tigres at the weekend.
Guadalajara's Dutch sporting director Dennis Te Kloese told reporters at Monday's practice that "the fact Benjamin is working, analysing and training is because he has to turn this matter round.
"I think no-one, fans, players or coaching staff can afford a defeat. We must win and play well," he said almost as an ultimatum.
The Chivas' owner Jorge Vergara's presence at the practice heightened the rumours Galindo's side must beat Puebla at home at the Omnilife this weekend to save his job.
Struggling UNAM Pumas confirmed coach Antonio Torres but there have been changes in the soccer management department with sporting vice-president Alberto Garcia Aspe sacked and replaced by Mario Trejo, who oversaw title victories in 2009 and 2011.
All three sides have made a poor start to the Apertura championship, first of two in the 2013/14 season.
Pumas, one from bottom, have taken two points from their five matches, Monterrey three and 11 times champions Guadalajara four.
Veracruz are top with 11 points while title holders America, whose victory in the Clausura in May handed them a record-equalling 11th crown, have seven with two matches in hand.