The trio of media outlets claim the Foxes will part company with current boss Claude Puel at the end of the season with Wagner the possible successor.
The Frenchman is facing a fight to hang onto his job following a huge slump in form which has seen Leicester win just two of their last 12 league games.
And the situation has been compounded by Puel's style of football proving unpopular with the side booed off at the end of both halves of their 2-0 home defeat to West Ham United on Saturday.
The 56-year-old was also taunted with ‘You don’t know what you’re doing!’ and ‘Sacked in the morning!’ chants.
In comparison, Wagner is well-revered by everyone connected to the club having worked wonders on a shoestring budget since becoming their boss in November 2015.
The 46-year-old followed up the Terriers promotion to the top flight for the first time in 45 years last season by being on the cusp of maintaining their top-flight status this term.