The 25-year-old Zambia striker has undergone surgery after suffering an ankle injury in Leicester’s final pre-season game with Lens last Saturday.
Cooper, who was named as Enzo Maresca’s replacement as Leicester manager in June, says he expects to be without Daka for some time.
The Foxes boss also said experienced duo Jamie Vardy and Conor Coady would be missing from his side’s opening game of their Premier League return against Tottenham on Monday.
“Patson is not great,” said Cooper.
“He’s had an operation and will be out for a few months. Vards has been injured since the second week of pre-season, he’s closer to returning but will be a little while.
“Conor Coady will be out for a few more weeks with his hamstring.
“Vards is at the latter stages of rehab. With his experience, he understands his body and will have a big say in that process of returning.”
Leicester start the season with the threat of a possible points deduction for alleged breaches of the Premier League’s profit and sustainability rules from when they were last in the top flight.
Cooper says the Foxes have no plans to sign any new players before welcoming Spurs at King Power Stadium.
“Every season you want to reinforce, you want to strengthen,” added Cooper. “We’re still going through that process. The club is working together and the communication lines are great.
“It’s been a slow market. Once I knew this week that there wouldn’t be any additions for Monday, I put that to one side and focused on Monday. That’s the only thing we can influence.”