The daily El Informador in the city of Guadalajara where Atlas are based reported on Saturday that former Argentina defender Cufre had been suspended by club president Eugenio Ruiz. It said Cufre had sought to get Asad removed.
"No one is above the club and we have decided to separate Leandro Cufre from the squad indefinitely," Ruiz was quoted as saying after Atlas drew 3-3 with Veracruz at the Jalisco stadium.
"We will notify him on Sunday and we'll pay him what remains of his contract but he's out of the team," Ruiz, a former Guadalajara mayor, told reporters outside the team's dressing room.
"All I can tell you is the club needs committed people and not against what we think. We want to change things and anyone not pulling the same way is not in our plans."
Cufre, 35, a former AS Roma and Monaco defender who was in Argentina's 2006 World Cup squad in Germany, joined Atlas in December 2011 from Dinamo Zagreb.
He was shown the red card for violent conduct after the final whistle in Argentina's penalty shootout loss to Germany in their 2006 quarter-final when he was an unused substitute.
Atlas are three from bottom of the Apertura championship standings with seven points and no wins in 11 matches.
Ironically, Cufre was suspended for Saturday's match because he had accumulated five bookings in previous games.
The team fought back from 3-1 down in the final quarter of an hour grabbing the equaliser through striker Edson Rivera in added time.
They were down to nine men at that stage after Flavio Santos was sent off in the 20th minute and Argentine Lucas Ayala in the 85th.
Title holders America lead the standings after beating Chiapas 3-1 on Saturday but fellow top teams UNAM Pumas and Guadalajara's woes at the other end of the table continued.
Pumas lost 1-0 at Atlante and changed places with them by dropping into the basement with five points and no wins in 11 matches.
Guadalajara lost 2-1 at Leon, who are in second place behind America on goal difference, and are four from bottom with seven points and a game in hand.