They were hammered 4-0 away by Chelsea in the Champions League on Wednesday to leave them bottom of Group D, below debutants APOEL Nicosia, without a win or a goal.
Things are just as bad in the league. Resino's side are 15th in the standings with one win from seven matches and they have La Liga's leakiest defence with 17 gpals conceded.
"It's clear from our position the situation cannot go on like this," Atletico president Enrique Cerezo told reporters in London.
"We have to find a solution immediately. Abel, as coach and as an Atletico man, continues to be the best in my opinion... but the fact is the results are not going our way."
Resino said he had no intention of quitting when questioned over his future after the Chelsea game, but the Spanish media have already started speculating over possible replacements.
Luis Aragones, Michael Laudrup, Quique Sanchez Flores and Bernd Schuster have all been linked with the post and another former coach, Mallorca's Gregorio Manzano, could provide the coup de grace, if Resino is still in charge on Saturday and loses.
The islanders have made an impressive start to the campaign and are fifth in the table, two points off the Champions League places.
Another coach feeling the heat is Ernesto Valverde at Villarreal, who host 19th-placed Malaga on Sunday still winless after seven games.
Villarreal slipped to the foot of the table last weekend after they were humbled 2-1 by promoted Xerez, who climbed above them with a first ever top-flight victory.
SURPRISE DEFEATS
At the top of the table, both leaders Barcelona and second-placed Real Madrid return to domestic action having suffered surprise midweek defeats in Europe.
Barca were stunned 2-1 by Rubin Kazan at the Nou Camp on Tuesday, and they will be out to shrug off suggestions that they have lost some of their spark, at home to promoted Real Zaragoza on Sunday.
The European champions struggled to a 1-0 win over Almeria, and drew 0-0 at Valencia before suffering their first reverse in all competitions this season, at home to Rubin.
"We didn't deserve to lose, but we have to learn from these errors," Andres Iniesta told a news conference. "This defeat should make us stronger for the coming games."
Daniel Alves has joined Thierry Henry on the Barca injury list.
Real Madrid, who are a point behind Barca, fell 3-2 to AC Milan in the Champions League on Wednesday, and seem to be missing injured top scorer Cristiano Ronaldo more than they would care to admit.
They visit Sporting Gijon on Saturday just before third-placed Sevilla host Espanyol.
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