The Kumasi-giants have already lost three times to Hearts this season, mounting pressure on them to win the game to appease their supporters.
They we're eliminated by Hearts in the semi-finals of the Ghalca G6 tournament in January before losing 1-0 and 3-1 away in the Ghana Premier League and 60th Independence anniversary Cup respectively.
"Kotoko shouldn't have a game on the July 2 but all of a sudden, they have come out with that President Cup game against Hearts of Oak on that particular day," Polack told Light FM.
"I think it isn't the right thing to do because we could play against Hearts six times only this year. Two in the league, another two game in the Independence Cup, President Cup and we may also face them in the FA Cup, which is too much for every team."
"So it's something that we need to discuss with the management before Monday. I'm against that and hopefully we won't honour the game," he added.
Goal sources have revealed that, Ghalca who are the organisers of the event have petitioned the owner of Kotoko, Otumfour Osei II to resolve the issue since the president of Ghana H.E Nana Addo Danquah Akufo-Addo will be the special guest of honour.