Bookmakers Betway and Paddy Power suspended the market on Conte becoming the next Premier League boss to be fired following a flurry of bets.
The Italian coach, who took over as Jose Mourinho's permanent successor in the summer, suffered a dip in September when his team recorded one draw and two defeats in the top flight.
The team recovered before the international break by sealing a 2-0 win over Hull City, but doubt over Conte's future has emerged.
According to Sky Sports News, Chelsea have described the rumours over Conte's future as "absolute nonsense" and insist that the 47-year-old is preparing for Saturday's visit of Leicester City to Stamford Bridge as normal.
The Blues are seventh in the table, five points behind leaders Manchester City.