The Blues boss enjoyed a successful first season at Stamford Bridge, winning the title and just missing out on a double with the FA Cup.
However, Conte has been left less than impressed with what has happened at the club since May.
Chelsea have struggled for progress with their transfer activity.
And the Blues have largely failed to land Conte’s top targets, including Romelu Lukaku and Alex Sandro.
Midfielder Tiemoue Bakayoko and centre-half Antonio Ruddier have both now signed for a collective figure of £74million.
Antonio Conte saw his Chelsea side beat Fulham 8-2 today in a pre-season friendly
Willy Caballero has also arrived on a free following his release by Manchester City, but Chelsea are still without a new striker.
According to The Sun, fears are mounting over Conte, with contract talks having stalled.
The Italian was expect to have signed new terms by now, but he is yet to put pen to paper.
There are said to be concerns Antonio Conte, who has been linked with a return to Italy, is becoming increasingly unhappy and frustrated.
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And one obstacle in particular faced over a new deal for the manager is the duration.
The Sun add it is unclear whether he will get a four-year contract or a shorter one.
It would be worth £9.6m a year, with Conte’s current deal expiring in 2019, having signed for three years when he arrived last summer.
Further star signings could help ease fears, but Chelsea face a busy period now with pre-season underway and the new Premier League campaign nearing ever closer.