Chelsea interim manager Rafael Benitez is unlikely to continue at the end of the season, after a difficult spell in charge at Stamford Bridge so far.
The Blues boss has struggled to keep pace with Premier League leaders Manchester United - Chelsea trail the Old Trafford club by 16 points - and Conte has been linked with both the Stamford Bridge job and the Real Madrid post.
Jose Mourinho's Bernabeu future remains uncertain, after a series of high-profile spats with senior Real Madrid players. The former-Chelsea manager even dropped captain Iker Casillas to the bench last month.
Conte enjoyed a hugely successful playing career with Juventus, winning five Serie 'A' titles and one Champions League, while he helped the Turin-based club to a unbeaten league season last term.
The defending champions now sit five points clear of second-placed Napoli, and Conte has been mentioned as a possible candidate to replace Benitez or Mourinho come the season's end.
And the Juventus boss, when informed of the reports, failed to play down the speculation.
He said: "I'm flattered. Both the club and I enjoy these assessments. It means that we are doing well."