Southampton then made it 2-0 on the hour-mark to leave Chelsea FC apparently heading towards another defeat, but goals from substitute Olivier Giroud and Eden Hazard ended up claiming a 3-2 win for Conte's men.
Germany global Rudiger was replaced by Andreas Christensen in the starting XI and not on the bench despite being fully fit, with Conte saying it was a "tactical decision".
The former Roma defender openly criticised Conte's tactics against West Ham after revealing that he believed they did not attack enough.
Rudiger said he had not intended it to be that but added that it was the likeliest explanation for his demotion from the team.
"I was a player, and the players must play every game, and not for me, but for the club, and for the fans", Conte said. But I didn't mean it that way.
"It was a fact, it wasn't about the tactics. This was a little break".
The Express report that the treble-winning Hoops boss is a serious contender for the job, with the Italian widely expected to leave Stamford Bridge just a year after lifting the Premier League.
"I don't know why the desire wasn't there but the coach is the first person to have the fault".
It remains to be seen if he would be tempted by a return to the Stamford Bridge, though the chance to prove himself in the Premier League again, should Chelsea be unable to land their other top targets, will nearly certainly give him plenty to deliberate.
Brendan Rodgers is one of four managers to be shortlisted as a contender to replace Chelsea head coach Antonio Conte at the end of the season.
"I think it would be a good reconciliation [with the supporters] with the FA Cup".
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