Henrikh Mkhitaryan capped his impressive start to the new season by equaling a Premier League record that had stood for 23 years.
Leicester nearly took A surprise lead in the 57th minute but De Gea's outstretched leg cleared away Riyad Mahrez's unsafe cross.
However, they came back strongly to post their first win against Brighton and Hove Albion last week. In the last five matches of Manchester United in English Premier League, UEFA Super Cup, and friendly matches, they have won four matches and lost one match.
Ibrahimovic is recovering from knee surgery, but the Portuguese boss added: "He will be back in January".
Also, with the Red Devils kicking off the domestic season with two convincing wins, Mourinho could be unlikely to make any changes to the playing XI.
In the 18th minute Juan Mata thought he had given United the lead but he was ruled marginally offside.
That came after Kasper Schmeichel had produced an inspired performance, saving Romelu Lukaku's second-half penalty as part of a fine individual display, with Leicester defending doggedly to remain in the game until the closing stages.More news: Jackpot! Winning $758.7M Powerball Ticket Sold in MA
The strikers Shinji Okazaki and Jamie Vardy have looked in good form, while there is a lot more solidity to this lineup than last season, when Leicester were all over the place in their title-defending campaign.
Leicester's summer recruit Vicente Iborra and defender Robert Huth are not fit enough to face Manchester United with groin and foot injuries respectively.
United have now scored 10 goals without reply so far this season and lead the Premier League heading into the global break, reports Efe.
Coming into the fixture, Leicester City have to be fully aware that it'll take a gigantic effort if they are to beat Manchester United in their own backyard.
United were dominant in the first 45, but flashbacks to the days of Louis van Gaal and Mourinho's maiden season were evident, as the hosts struggled to break down the 2015/16 league champions.
In Paul Pogba, United have their leader in style if not in name.
Against the form team in the league, Leicester put up a decent display and while they did eventually come away from Old Trafford with nothing, they will have to take solace from the fact that now it's hard to deny this United side a win.