Da Silva, nicknamed 'Polilla' (Moth), is expected to take over at Penarol from Gregorio Perez, who was sacked on Sunday, club vice-president Edgard Welker told Reuters.
"Da Silva is Penarol's number one choice for the coaching job," Welker said.
The 50-year-old Da Silva surprised Banfield by telling them he was quitting after only three matches in charge and having ended the team's six-match losing streak with a 2-1 upset win at Racing Club on Sunday.
"Club Atletico Banfield inform that the Uruguayan trainer left his post to take on the coaching of Penarol of Montevideo after saying it was one of his life dreams to coach there," the Argentine side said on their website.
Keen for a long time to coach his home city club, former Atletico Madrid and River Plate striker Da Silva is due to meet Penarol officials in Montevideo on Tuesday to discuss the terms of his contract.
Penarol, runners-up last year in the Libertadores Cup, have made a very poor start this year to South America's elite club competition, which they have won five times.
They lost their first two group matches, including a humiliating 4-0 defeat by Colombia's Atletico Nacional in the Centenario in Montevideo last week.
Banfield, who signed Da Silva in December after sacking former Mexico coach Ricardo La Volpe, finished bottom of Argentina's Apertura championship in the first half of the season and lost their first two Clausura matches.
In his coaching career since 2007, Da Silva has also worked at Defensor Sporting in Uruguay, Al Nasser in Saudi Arabia and at Argentina's Godoy Cruz.
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