Manchester United manager Louis van Gaal has refused to rule out the possibility of signing goalkeeper Victor Valdes.
Manchester City boss Manuel Pellegrini says he is confident that England goalkeeper Joe Hart will sign a new contract.
The goalkeeper has been heavily linked with a move to the Premier League this summer, with Hull seeing as many as three bids for his services rejected by the Foxes.
That sparked speculation that Schmeichel had requested a move away from the King Power Stadium but the 26-year-old insists that is nonsense.
After a hectic summer of international duty with Denmark which followed Leicester's play-off heartache, he remains as committed as ever to the club and helping to realise their own top-flight ambitions.
"It's been a strange summer, coming to terms with what happened to the team at the end of last season and not getting much of a break due to internationals, but there has never been a thought in my mind that I wouldn't be coming back to Leicester," Schmeichel told the club's official website.
"I've said many times before that I enjoy playing for this football club, I enjoy coming to work every day and I want to be successful here.
"You hear speculation of things you're supposed to have said or done like handing in transfer requests and it's just ridiculous. I've never said I wanted to leave Leicester.
"Like every professional, I want to play at the highest level, but I want to do that with Leicester and, with the players, management, staff and fans we have here, I know we can achieve that.
"It's a big season coming up for us now. We need to make sure we're focused on what we want to achieve and work harder than anyone else to make sure we achieve it."