The 55-year-old Manzano's departure came after less than half a season in his second stint at the helm while former Atletico midfielder Simeone said he was ready to take over after quitting as coach of Racing Club in his native Argentina on Tuesday.
"The executive board of Atletico Madrid, in a meeting on Thursday to assess the sporting situation, decided unanimously to dismiss Gregorio Manzano as first team coach," the club said on their website.
President Enrique Cerezo told reporters the 42-year-old Simeone, a fan favourite as a player, was enthusiastic about their offer and the club are expecting his response by Friday.
"We have only made an offer to Simeone," Cerezo added.
Manzano, who has also coached Real Mallorca, Sevilla and Malaga, returned to Atletico in June, coinciding with the departure of prized forwards Sergio Aguero and Diego Forlan and the arrival of striker Radamel Falcao and midfielders Diego and Arda Turan.
Known as 'the professor', he has overseen an erratic campaign including a 5-0 league drubbing at Barcelona.
Atletico, who would usually be challenging for a European qualification berth, are 10th with 19 points from 16 matches and there is widespread discontent among fans about the way the club are being run.
At the end of the 2009/10 season their debts totalled 452 million euros, compared with revenue of 480 million, according to a study by a University of Barcelona accounting professor published in June.
At a news conference after Wednesday's 1-0 home defeat (3-1 on aggregate) by Albacete, Manzano apologised to the fans, his players and the board.
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