According to Nhyira FM in Kumasi, the former Black Stars coach has decided not to stay as head coach of the Porcupine Warriors when the season ends.
Kotoko has two games remaining in their 2020/21 Ghana Premier League season.
Bechem United will host the record Ghana Premier League winners at Bechem Park before finishing the season with a home game against Elmina Sharks.
Barreto, on the other hand, has been under severe scrutiny following Kotoko's 1-0 loss to arch rivals Hearts of Oak in their matchday 31 games.
The loss dealt a significant setback to Kotoko's prospects of winning the league title.
After 32 matches, Hearts of Oak top the league table with 59 points, while Kotoko are in second place with 54 points.
The 64-year-old was employed in March 2021, just before the second half of the season began, to replace Maxwell Konadu, who was fired in December 2020 after only five games.