Simeone quits San Lorenzo
Simeone and San Lorenzo's board of directors had come to a mutual agreement for the former Argentina captain to leave the club he took charge of a year ago, they said on their website.
"The decision was Simeone's, although it's by mutual accord with the directors," club Vice President Guillermo Zoppi was quoted as saying.
"It's the best thing for the club," said Simeone, quoted by sports daily Ole on its website.
San Lorenzo, one of Argentina's traditional "Big Five", are 17th in the Clausura championship with 11 points, 16 behind leaders Independiente, who beat Arsenal 1-0.
Midfielder Sebastian Romero scored the only goal at San Lorenzo's Nuevo Gasometro ground after five minutes.
The 39-year-old Simeone, who won league titles with Estudiantes in 2006 and River Plate in 2008, had been at a loss in recent matches to find a way out of trouble for his team.
Former Mexico coach Ricardo La Volpe has emerged as a strong candidate to take over.
Independiente went seven matches unbeaten and opened up a five-point lead with their home win courtesy of a fine goal from Leonel Nunez, the striker's third in as many matches.
Argentinos Juniors climbed to second on 22 points with a 2-1 win over Chacarita Juniors, Facundo Coria scoring both their goals.