The Dane was reportedly being watched by a number of clubs after a solid first season in the Premier League with the Foxes, but the Gunners were said to be particularly keen, according to the Daily Mail.
Manager Arsene Wenger is believed to be in the market for a goalkeeper this summer, with doubts over whether David Ospina is a long-term solution and Wojciech Szczesny having fallen out of favour this season.
A move for Schmeichel would not come cheap though given he signed a contract to stay at the club until 2018 last summer, and he has now quashed any talk of a move away.
“I've played for four seasons in Leicester, and they are happy with me, and we have a good working relationship," he said.
“This is where I see my immediate future. A club transfer isn't in my thinking. I am in a club where there are good coaches and owners, and it's great."
The 28-year-old managed six clean sheets last season, with five coming in the last seven games, helping them from bottom of the Premier League table to a 14th-placed finish in an extraordinary end of season run.
Whether he would be an upgrade on what the Gunners already have though is questionable and they need a world-class 'keeper if a title challenge is on the cards next season.