The Blues lead the Premier League by 10 points with 11 games left to play and Conte has inspired an incredible turnaround after the 10th place finish last year.
The Italian replaced interim boss Guus Hiddink in the summer after Jose Mourinho was sacked in December last season.
Antonio Conte is set to sign a new contract at Chelsea
Antonio Conte has got Chelsea back on top in the Premier League
Express Sport exclusively revealed last week that Conte was in talks over a new bumper deal as Inter Milan began circling.
The Serie A side were keen to jump on Conte's homesickness after he revealed he missed his family back in Italy.
But now Sky Sports claim he will sign the deal in 'a matter of days'.
Conte struggled at Stamford Bridge to begin with and faced crisis talks with owner Roman Abramovich after the home defeat to Liverpool in September.
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A week after that they were beaten 3-0 by Arsenal but Conte changed the shape to a back three at half time and has stuck with it ever since.
The Blues then surged forward to top spot and have looked unstoppable.
Eden Hazard has been in sensational form and, following Monday's win over West Ham, said: "This season we have all reached a high level, me included.
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"We are happy to play together. Last season was hard but two years ago was a great season.
"There are similarities with what we did two seasons ago and we want to do the same thing and get the title.
"But in England it’s never over until it’s over. You never know what’s going to happen. We will all give everything until the end to try to win the league."