Vucetich, speaking after his side maintained the Mexican Championship's only unbeaten record with a 2-0 win over Torre's Toluca, told reporters: "Late (Friday) night was when I decided definitely to step aside.
"The motives for taking this action are personal and more than anything family."
Toluca's De la Torre is now expected to be announced as Mexico coach on Monday with the remit of steering his country to the 2014 World Cup in Brazil amid a conflict between national team players and the Mexico Football Federation (FMF) management.
"I think he is the strongest candidate there is, I wish him the best of success, I think he will fit perfectly in the national team," Vucetich told Televisa.
De la Torre's brother Nestor resigned in midweek from the job of national teams director after players revolted against sanctions he imposed on team members who held an unauthorised late-night party following a September friendly.
Mexico have been under interim coaches for friendlies since the World Cup in South Africa where they were eliminated in the second round by Argentina and Javier Aguirre quit more than three months ago.
Speaking ahead of Monday's decision, De la Torre told reporters: "If I was not ready I'd have quit (the race) already but let's wait for the federation to make it official."
CLEAR LEAD
The victory by Vucetich's Monterrey left them four points clear at the top of Group One of the Apertura championship with 26 points from 12 matches. Santos Laguna, beaten 3-0 at home by runaway Group Three leaders Cruz Azul, are second.
The 18 teams play each other once in the round-robin phase of the championship regardless of which of the three groups they are in. The top two in each group plus the next two best-placed teams go into the knockout phase.
Group Two is led by San Luis, who have 19 points after their 3-2 win over Queretaro, with Toluca two points behind in second place and America hovering a point further back before their visit to Puebla on Sunday.
Cruz Azul, with 28 points in Group Three, are 12 clear of second-placed Chiapas, who were away to Pumas UNAM on Sunday.
Concacaf Champions League title holders Pachuca, fourth in Group Two, were held 1-1 at home by Morelia, whose defender Juan Carlos Reyes saved a penalty after taking over in goal following the dismissal of their Colombian keeper Miguel Calero.
