The Foxes are on the lookout for a new manager after parting company with Shakespeare on Tuesday afternoon, bringing an end to the popular coach's spell in permanent charge just four months after appointing him.
Wagner is understood to have been high on Leicester's list of potential replacements, having also been tipped to take over in the summer, but the 46-year-old has no intention of leaving the John Smith's Stadium.
Asked about the speculation, he told reporters: "It is not a distraction and it doesn't bother me. I am and I will be the manager of Huddersfield Town."
Wagner was appointed by Huddersfield in November 2015, earning promotion to the top flight in his first full campaign at the helm.